Is restoring my MacBook Air to factory settings a wise decision?

Using TM won't complicate anything. It conveys only advantageous options.

To be clear, the workaround I'm describing is as follows:

1. Back up the Mac with Time Machine: Back up your Mac with Time Machine - Apple Support
2. Erase the Mac as described in Use Disk Utility to erase an Intel-based Mac - Apple Support
3. Boot Recovery, and reinstall macOS using the key chord that corresponds to installing the latest macOS version compatible with that Mac (details described under "On any other Mac" in How to reinstall macOS - Apple Support). That will be Sonoma for a 2019 model MacBook Air.
   1. If you don't want Sonoma, you would need to reinstall its originally installed operating system, whatever that was, probably Mojave, after which you could upgrade in increments if you so decide to do that.
4. When the installer finishes, it will ask if you want to restore its content from the Time Machine backup. At that point you have the option of choosing to restore everything (the ideal choice) but if insufficient space still exists, you can choose among broad categories of items to restore.

Bear in mind the Time Machine backup will be the only repository for the entire contents of that Mac, so it's imperative that it is intact. Personally I don't do anything without at least two redundant backups.

By the way, what's the capacity of that MacBook Air? The reason for asking is that the workaround I described is often the only way to upgrade macOS with a 128 GB startup disk (for example). If your MBA is a model with 256 GB or more built-in storage, you can probably find enough files and / or apps to delete to increase the space you need. Refer to Free up storage space on Mac - Apple Support.

Bear in mind that if you use Time Machine to back up your Mac, and you then go about deleting files and folders, the next time Time Machine performs a backup it will consider anything that you deleted fair game for deletion on the backup. So, the way to address that contingency is to:

1. Back up the Mac (and be sure to wait for it to finish),
2. turn off Time Machine,
3. delete whatever you want to delete, then
4. attempt the macOS upgrade again.

• Note regarding Step 3: When you delete files from an APFS formatted volume including emptying the Trash, it takes macOS some time to actually release the space formerly occupied by those files. The generally accepted amount of time for that to happen is about a day. In my experience it has never taken nearly that long, but some people have reported otherwise. The point is the space will not be freed immediately, so we need to wait.

If that method is successful then you can use Time Machine to selectively restore what you want to restore: Restore items backed up with Time Machine on Mac - Apple Support. Just don't allow Time Machine to back up until you're certain the end result is what you want.

Finally, don't forget to turn Time Machine on again.

I agree with John Galt but I do have a couple observations. After you’ve erased the computer and installed the OS - upgrading to a newer version or not - you’ll be prompted to use Migration Assistant to move your backup to the computer. If you want to avoid running out of drive space again you’ll want to move less stuff back onto the computer which leads to a couple issues:

1) Migration Assistant will copy all your applications to the computer, you cannot pick and choose. You may want to consider installing your applications by hand if you have apps you no longer use.

2) Migration Assistant gives you some flexibility when choosing which data files to transfer but you don’t have the ability to pick and choose which files but TimeMachine does. I recently moved into my new MBAir and copied all but 2 folders with Migration Assistant, then afterwards used TimeMachine from the desktop to move some files from a couple other folders.

3) If you decide to not copy one or more folders you need to remember that TimeMachine backs up the computer as it exists now. It does not archive older files if you delete them and files you delete from your computer can later be deleted from the TimeMachine backup. Say you choose not to copy the folder Dumb Stuff. A few months from now the backup drive may run low on space so TimeMachine may delete the Dumb Stuff folder because it isn’t currently on your computer. Oops, that isn’t what you wanted. For this reason I use 2 backup methods. TimeMachine is my every day backup and once a month I back up with a different program that does keep an archive. Nothing gets thrown away, ever unless I do it manually. (I used to back up weekly but I’m retired now and mostly is my new weekly)

Yes; in fact it is the most practicable solution. Be sure to save everything you need as you wrote. Consider using Time Machine to do that: Back up your files with Time Machine on Mac - Apple Support