do i need to delete an OS before upgrade?

You cannot add storage. You can use an external SSD or HDD to move off some files and allow space for an update. Also, if you use Internet Recovery (boot up with command-option-R pressed) to update, you need less free space (a MacBook Air needs ~38 GB free for a MacOS 12 Monterey update from Big Sur, but only needed ~27.5 GB free with Internet Recovery.

As an aside: you need to maintain a minimum of 15 - 20 GB of empty storage space on your disk at all times for the OS to function properly - your "storage" space also houses the entire OS and all of its system files - they need space to read/write at all times. If you fill it up completely, the computer will eventually stop functioning.

So, get an external drive and move all your space hogging files to it permanently - then delete them from the internal.

Excellent points. However, MacOS system files tend to bloat, especially on the MacBook Airs for some reason (or maybe I notice it more on my kids' because they have less storage. "Other" has been renamed System Data, but it still bloats. One of the MBAs had System taking 30 GB.

In one case, freeing up just enough space (27.5 GB) to update to Monterey with Internet Recovery resulted in a 'fixed' System folder and a post-update free space of >40 GB.

Good to know; I tend to blame the "other" category bloating on TM snapshots - why? Because I don't have a problem on either my MBA (Monterey) or iMac (High Sierra) with that ----- I don't use TM; never opened it. So, I have no snapshots either. I prefer clones - have at least two of each OS version I am running (or the Mac is capable of running).