I invented a very fast string search algorithm based on bloom filters. Our paper [1] was accepted to the Symposium of Experimental Algorithms 2024 [2]. Code can be found here [3].
[1] https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.S...
If you want guaranteed linear performance in the worst case too, then LinearHashchain is the one to use. It is slightly more complex to implement as it builds in a KMP style verifier to make it linear (so almost two search algorithms are needed). It is actually about as fast as HashChain generally in the average case, so you don't lose out.
The others are either experimental or quite niche and not suitable for most purposes. SentinelHashchain is actually the fastest, but relies on being able to add a copy of the pattern at the end of the search text. Mostly this won't be possible in most search contexts, unless you control all memory allocations.
So I'd start with HashChain, and maybe play with the linear version later - most of it is the same, it just needs a bit more adding.