Contacts app not working on Bigsur

The Application " Contacts " is part of the Operating System of Big Sur. As such a]can not be reinstalled except by reinstalling Big Sur.

An Aside - your profile is showing MacBook Air 13″, macOS 11.2. There is an update available to 11.4. Do not know if this has any bearing on your issue.

as mentioned, you would need to reinstall big sur to reinstall contacts. before going through that, i'm thinking you should download and run the free version of EtreCheck so we can see if you have some software installed that is causing your issue. make sure you give "full disk access" to etrecheck. read how to use it by reading Using EtreCheck. you can see how to post the report here by reading How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report. and it automatically obscures sensitive things (like serial numbers) so you don't have to worry about sharing the report here.

After upgrading to Big Sur 11.4 my problem with contacts app freezing was fixed...

Good fixed by updating to latest available Big Sur 11.4

My MacBook Air (early 2015) has 14.1 installed already; I can't restart or shut down because of the frozen Contacts. Don't know how to proceed from here. Obviously, no Safe Mode. Advice?

My apologies; it's late in the day. It's amazing what a Force Quit will do.