My apple Watch vibrates but doesn't give me time to double click

Do you mean you want your Apple Watch to unlock your MacBook Pro, without having to use either TouchID or type your passcode into it? If yes, one does not need to double click anything on the watch to unlock a MacBook Pro.

Have you updated your Apple Watch to WatchOS 9.5 and MacOS Ventura 13.4, which were both released this week and specifically addresses this?

Also to be clear, with Unlock your Mac with Apple Watch, there has never been a need to touch the watch. It does vibrate, for sure, but touching the watch has never been part of it. Just wearing the watch when you go to unlock your MBP, should unlock your MBP. But you do need to update both devices to fix this.

I don't know what software you've got running on your MBP, but you've got something that is not playing nice on it. For example, if you use ANY cleaner software tools, or anti-virus tools, they can mess up a MBP big time. You may be using a VPN, which may be preventing things from running smoothly.

What exactly is it you are trying to do on your watch with your MacBook Pro?

Restart both your MacBook Pro and Apple Watch. This is something you should do after every OS update, anyway.

And it did or didn't fix the issue? If no, contact Apple Support for more help. It works fine with my Apple Watch Ultra on my MacBook Pro M1 Pro. I'm thinking you have an issue with your MBP.

Don't just turn off the unneeded software, get rid of all the bloatware on your MBP. You don't need any of it. I'm glad your watch vibrated and you're welcome.