replacing operating system on MacBook Air 2015

Big Sur should have no issues, but a 2015 MBAir should be able to run macOS 12.x Monterey as well just like @MartinR mentioned. If Monterey is not showing up as an option in the Software Update System Preferences, then you can use the following Apple article to get links to download various versions of macOS installers (as long as the computer is compatible with that installer):

How to download and install macOS - Apple Support

The only things you have to worry about is the 32 bit app support already mentioned by @MartinR and also whether the other 64bit third party software you use is compatible with Monterey or whatever later OS you want to use. Also make sure any external devices are also compatible especially if they require drivers to operate. If you are using the original Apple OEM SSD, you are fine, but if you are using a third party internal SSD, then Monterey likely will refuse to install unless you still have the original Apple OEM SSD handy.

Make sure to have a good backup before attempting the upgrade just in case something goes wrong. You should already have frequent & regular backups anyway.

I would also recommend creating a bootable macOS USB installer as well just in case something goes wrong during the upgrade so you have more options. While you have an option to use Internet Recovery Mode to access the online macOS installers, this requires a good network connection (routers, ISP, and local Internet issues can cause problems).

Your 2015 MBAir is probably qualified to go all the way to Monterey. Whether or not Catalina is the "best" replacement is a subjective matter.

Regardless, be sure to check all your apps first. Older "32-bit" apps that run on High Sierra will not run on Catalina or later versions of macOS. You can use GO64 to check your apps for compatibility.

It also depends somewhat on the specs for your MBAir. Specifically, how much RAM & disk space does it have?

You could choose to upgrade to Catalina first and then later to Big Sur if you feel it's ok.

Just make sure you have a good backup of your data before you upgrade.