Practical take: Thompson sampling is great. Use it if your main focus is getting things done. I found that most literature about MABs concentrates on various (mostly not too useful) approaches to MABs instead of on getting stuff done. Which is of course fine if your intent is to study MABs.

Thompson sampling is easy to implement, predictable, stable, and you can leave your experiments running forever without supervision. It has very few drawbacks.

With a combination of two HyperLogLogs and a Bloom filter, you can also have a really nice scalable distributed implementation (HLLs and BFs combine in an idempotent manner, so updates are lock-free), albeit at the cost of low precision early on as the number of samples is low.

Don't use a library. Thompson sampling itself is not difficult (specifically, 6 lines, as I'm looking at my Clojure code), you will need to understand it very well anyway, and most libraries will include lots of superfluous garbage. Most of the work is not with Thompson sampling, but with processing your events, and that is something which is application-specific anyway and can't be abstracted well.