Does migrating backup to mac also installs all my apps with its settings.

Below is IMHO

If the new computer is going to be the Apple Silicon M1 / M2 Equipped Computer - would suggest Only Migrating the User Account and nothing more.

Some have had success and others have been left with a mess when Migrating everything.

1 - Apple Silicon with either Big Sur macOS 11 or Monterey macOS 12 Only Support everything 64 bit and there is no workaround.

2 - Issues that may exist on the older computer will be migrated to the New Computer. This would badly pollute the new Original and Pristine installation of the new OS.

3 -  Applications, extensions and Software Drivers may or may not even work on the new computer.

4 - IMHO - it would be best to only install new application etc Directly from the Developer or the Apple Apps Store.

5 - Due Diligence on New Applications and make sure they are Monterey / Big Sur compatible and factor in the ARMs CPU of the Apple Silicon Computer  

Yes, at least in theory. That is what Migration Assistant is designed to do. Move your content to a new Mac - Apple Support is offered when you initially set up a new Mac. Even though it is time-consuming, that is the best time to do it.

However, some apps are designed to be installed on one and only one Mac and are tied to its unique identifier, so transferring information from an older Mac to a new one may require a new license for apps that require one. The only products that I believe will that do that are from Microsoft, so if you use MS Office or such products you may need to contact them to determine if your existing license can be transferred to your new Mac.

But what you describe is the way I have set up all my new Macs, going back to the 1990s at least.