I was thinking and I thought , that, if you would use the Jade ring and SCP-106 would start coming out of the floor, why should there not be a way to hide. You are going to tell me that he can "feel" you but not with the jade ring. So just crouch and hide then he comes back in the floor.

To my knowledge the Jade-Ring SCP-714, has no effect on 106's behavior whatsoever. He makes you immune to 895's hallucinations, yes, but how would it work with 106?
You can "hide" from Larry my backing out of the room and/or crouching very quickly from what I know. But there's always a chance of him seeing you anyway.

So you're saying you want the option to potentially hide from 106? I think losing him is already easy enough as it is, as he's been slowed down immensely over time.
If anything, he needs to be more aggressive and more difficult to lose.

This is not how 714 works. The effects of the Ring include:
The effects would not hinder any of 106's abilities. The ring does not have any effects to anyone other than the wearer. 106 does not just "know" where anyone is. If he does not see you, he does not follow you. The only reason he appears in the game is because he is supposedly stalking you, waiting for the best moment to attack.

Omniary: fuck you anglerfish can't smell
Dr. Trialtrex21: how you know bitch
Omniary: it probably could smell you though
could probably smell your fucking dank ass nasty powersuit structure gel trog ass enslaved protein bullshit sloshing in your suit from a mile away

Better A.I for SCP-106

Yeahhhh I see........

The AI is fine in regards to him finding you. Like Trex said he doesn't know your exact location but, very much like most creature with eyes, he can see you. If you aren't fast enough to hide when you see him, well, that's your fault.

714 with 106? What the..?

Your idea is not to have a "better AI" for 106 but an additional difficulty and making the ring useless. For me, a "better AI" is to make those black -disgusting- hole when he goes through a wall while he try to catch you to make this more realistic with 106(I know its not like to improve his AI but his mechanic).