reboot suddently of my Mac ,behaviour noticed since I replaced the battery

That AHT error is almost certainly the result of something Apple did a while ago with a software or firmware) update. Read macOS (10.14): Disables AHT, Apple Diagnostics on Select Macs.

That means you will not be able to use AHT to diagnose anything on your own.

As disappointing as it is, that fact is not as bad as it may seem. Even if AHT worked, it concludes with only two broad categories of results: either "no trouble found" despite the fact trouble obviously exists, or it will identify a specific fault that only Apple would be able to fix anyway.

A possible alternative is to hold option D on startup. That will force the Internet version of AHT to load. Refer to Use Apple Diagnostics to test your Mac - Apple Support, under "Learn More".

Given those limitations, I recommend accepting that dealer's offer to replace your Mac's battery. However, before doing that, ask if they can also run diagnostics using utilities available only to dealers. If they can positively identify the meaning of that -2 code, you may avoid paying to fix something that isn't broken. An inoperative exhaust fan (for example) is an inexpensive repair. It could be something as simple as a piece of dust or mechanical interference preventing the fan from rotating.

That -2 code means something, so have them determine it. It's always best to avoid replacing things without justification.

2-24 11:14:17.094497+0100 0xb7    Default   0x0         0   0  kernel: (AppleSMC) Previous shutdown cause: -2

Although Apple does not provide exact descriptions of those codes, negative shutdown codes are generally accepted to implicate defective hardware. The only known exceptions to that apply to expected events such as a firmware upgrade.

Negative shutdown codes can occur due to transitory conditions, such as an SMC-forced shudown for an overheat condition. They should cease after addressing whatever caused them to occur.

Known shutdown codes include 5 indicating a "normal" shut down, and 3 indicating a "forced" shutdown. Your log shows both of those examples, but the -2 is most likely hardware-related, and those were the two most recent log entries.

You appear to have correlated those events to the recently performed battery replacement. If Apple or an authorized Apple repair shop performed that work, take it back to them and tell them to fix it.

All Apple service begins with Get Support.

Is it a Catalina re-install that will delete some files like Chrome Bookmarks or something or unrelated ?

Reinstalling macOS is nondestructive so it should leave those files untouched, but it just goes without saying that you should have a backup (Time Machine or the equivalent) anyway: Back up your Mac with Time Machine - Apple Support.

That negative "Previous shutdown cause" is still appearing, so defective hardware remains the likely cause. It's unclear to me whether Apple replaced the fans or not, and I think their recommendation to reinstall macOS amounts to wishful thinking. Did they say anything about the fans? It should be easy enough for Apple to test them for operation.

It is certainly possible that -2 code could indicate something other than defective hardware, but it would be the first I've heard of it.