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Sonic Origins is great on its own, while this DLC's appeal is niche.
It would be recommended to long-time fans who would get a kick out of playing as Amy in the classic Sonic series. Yet the added Mirror Mode is redundant and the "Extreme" Missions are rather easy. There is also the addition of art/music from Knuckles' Chaotix and Sonic 3D Blast, despite those games not being included in Sonic Origins. The handful of remixed tracks are alright, but are not substantial.
The DLC would mainly be recommended to existing fans that might enjoy rummaging through the largely mediocre Game Gear titles.

Sonic Origins Plus' Game Gear Games

In short, the Game Gear library here is mostly a drag. Several games have serious issues and lack polish.
It is interesting that these games are different from any Sega Genesis counterpart. They commonly share some mechanics and themes from the Genesis games, but they were independently developed due to 8-bit hardware limitations. The only exceptions to this are Sonic Spinball and Mean Bean Machine, where they are direct ports of console games.
The following are reviews of each game, with the intent to highlight any positive and unique aspects of them.
Sonic the Hedgehog
This handheld title feels more like a prototype than a finished game. The gameplay is a serviceable platformer, but without most of the speed-oriented mechanics and levels. The graphics and sound are oddly charming, even though they are somewhat crude. The boss battle stages also do not allow the player to collect rings for protection, which doesn't seem fair. The player also loses all rings permanently when hit, which is a bummer.
Most of the experience is quite jarring, so it's only recommended for those who have exhausted all other content in Sonic Origins.
Sonic the Hedgehog 2
It is easy to compare this game to its predecessor, but it is definitely an improvement in nearly every regard. The game runs well, rewards speed, and has nice visuals/music. However, the boss battle zones can be rather challenging, since again there are no rings anywhere. Thankfully, continues are given generously and extra life items are abundant.
Overall, this best captures the appeal of a bite-sized Sonic game.
Sonic Chaos
This entry seems a bit redundant compared to the previous entries. It is a quick and relatively easy game, aside from a couple tricky Chaos Emeralds to find. The game features a playable Tails, which is neat. Much of the game can basically be skipped by collecting 100 rings, which warps the player to a special stage instantly, which then ends the normal stage. The bosses are very simple, and their stages have rings to use to protect against them.
Sonic Chaos is a decent experience, but it is derivative of the other Game Gear platformers.
Sonic Triple Trouble
This handheld take on Sonic 3 holds up okay. The gameplay remains a little slow, but is a passable experience. The graphics are quite nice. Surprisingly, the final special stage is relentless, as there are many obstacles that can render the level unfinishable. Luckily, the boss battles are pretty easy, with many opportunities to gather rings beforehand.
It's cool to see the introduction of the obscure villain "Fang the Sniper" here. Otherwise, this game is not very remarkable.
Sonic Blast
Despite the ugly art style and bland music, the game can be a decent time. To be specific, the pre-rendered sprites of Sonic are generally awful. They have odd positioning, a low animation framerate, and have strange lighting artifacts. A pleasant surprise is that this game seems to run better than any of the other Sonic platformers here. Its levels are basic and are not difficult to complete.
The game can be a fun enough experience, so long as the character sprites are tolerable to view during play.
Sonic Spinball
This janky port can be somewhat enjoyable. The concept of a Sonic pinball game where the player can directly affect pinball movement has merit. While the framerate is low and inconsistent, the game is forgiving. The graphics and sound are lackluster, but are not offensively bad. It can be worth giving a go if the player can adjust to the wonky game physics.
Sonic Drift
This simple racing game is decent. Getting the hang of the titular drifting mechanic is satisfying. The game doesn't pose much of a challenge, as the rival racers are predictable. The graphics are alright, and the music ranges from okay to somewhat annoying. It's worth a quick look.
Sonic Drift 2
A step up from the previous iteration, certainly. There are more racers, track obstacles, and a new rubber-banding enemy system that is more chaotic. Causing a rival racer to rear-end the player is cathartic. However, the view distance ahead and behind the kart is very low, making it difficult to tell what/where are the power-ups, obstacles, and other racers. But the tracks at least have neat effects and themes, utilizing pseudo 3D objects and parallax scrolling.
The random enemy behavior and low draw distance can make it frustrating to complete. Besides that, the game can be enjoyable in short bursts.
Sonic Labyrinth
This maze game is actually quite fun. When accustomed to the controls, it is exhilarating to zip through each level. The game performs well technically and the pseudo 3D graphics are interesting. Despite having a couple of strange requirements to get the "best" ending, the game is a neat experiment that can yield positive results.
Tails' Skypatrol
A unique "ring-em-up" game starring Tails. The gameplay is interesting, and can quickly veer from being very easy to difficult. Sometimes it's best to just smash the attack button as if it were a normal shoot-em-up. The graphics are very good and add a sense of charm. The game is a fun time, despite lacking substance.
Tails Adventure
Another experiment with Tails, this time being an exploration-focused game. It's nice to roam around Tails' home island and fend off the invading robo-ducks. There are dozens of items to find in the levels, including some heavy weaponry like napalm bombs and proton torpedoes. While only a handful of items are required or useful, it's entertaining to see such an innocent fox cub become so armed to the teeth. The visuals are great and are very detailed. The music is average, but doesn't detract from play.
Using a guide to finish the game is recommended, as it could become easy to get lost. With that handy, this game is a substantial experience compared to the other Game Gear titles.
Dr. Robotnik's Mean Bean Machine
This bean-counting puzzler port is pretty good. Once the player gets accustomed to the matching mechanic, it's gratifying to see Robotnik and his cronies be foiled. It really only takes one good combo to finish any stage. The graphics are quite wacky, but have personality. This version also contains an exclusive Puzzle Mode, which is a good challenge.

Conclusion

The platform games, which should be the highlight of this collection, have many glaring issues. They generally don't run well and can have input delays. It's usually not advantageous to run fast during gameplay. The low resolution can cause frustrating mistakes. Sonic 2 on Game Gear thankfully has the least issues, but it is still amongst many other lackluster experiences.
The spin-off titles are at least more interesting. Some of them can be enjoyable, such as Sonic Labyrinth or Tails Adventure. But the player must buy the entire collection on the chance they might enjoy just a couple of them.
Many of these games, especially the platformers, don't offer a meaningful experience. For the sake of historical preservation, their inclusion is welcomed. But in the interest of the gameplay experience, the DLC is not fully recommended.