my safari is not working. what should I do?

Safari is built into the OS can not be removed or deleted.

Does the same issue present when booting into Safe Mode ??

Safe mode may help you resolve or isolate problems that you’re having with your Mac.

When you start up in safe mode, your Mac prevents some software, such as startup items, from loading, and it performs a check of your startup disk. Your Mac may take longer to start up because of the check.

No, you can't delete Safari. However these are the common problem why Safari isn't working.

• Too many tabs opened
• Too much cache, downloads, and history logs that have not been cleaned for a long time
• An extension, plugin, or website you're browsing is causing Safari to crash/freeze
• An outdated version of Safari 
• Older version of macOS

You can do this if ever:

Close all tabs (Open Safari > Close all tabs)

Clear website data (Go to safari > Preference > Clear data)

Check Updates (About this Mac > Check updates)

Or lastly, Remove website data from Finder

1. Go to Finder.
2. From the Go menu, select Go to Folder. 
3. Enter ~/Library/Safari and click Go.
4. Remove all files that contain History.db in their name and a file LastSession.plist.

Those are just suggestions. Up to you mate. :)

In addition to what P. Phillips said: there may be other software causing problems. To ascertain what the cause may be, we need more information. Please run Etrecheck and post its full report here.

Use the “additional text” button and paste the report into the text box.

If Safe Mode does not isolate where the issue is - suggest following the very good suggestion from @ Luis Sequeira1.

It is my understanding - even Apple Support persons have used this Software Tool to Trouble Shoot.

I had the same issue.

You could try Safari 15.1 beta > https://developer.apple.com/safari/download/

Have you tried quitting the Safari, then open again?

Maybe you can try rebooting your device as well.