Besides the customary "UPDATE TO SONOMA" there are smaller updates available
but almost hidden!
Go under System Settings -> Software Updates Available
Look for this, way down at the bottom of the "fabulous features" list.
You may find updates to (for example) Ventura and Safari under More Info...
These no doubt have to do with security fixes.
This will not happen for really old versions of MacOS, which they stop updating.
P.S. in the terminal, you can type "softwareupdate -l" to list available updates.
I won't say how to actually apply them, because you gotta know what you're doing before messing with updates from the terminal.
(It's on the Apple support site, or "man softwareupdate" at the terminal.)
NOW as for compatibility with websites.
A pain in the ass.
An up to date Opera Browser was flagged as obsolete or whatever by a site or two.
I use Opera because it takes almost every chrome extension, which is kinda cool.
I found, for that site, that my semi-functional Safari browser started working fine when I went under Develop -> Disable Extensions for that site. After all, I just wanted to access my account to find the balance, or pay something, rather than surf random sites with ads from hell.
You will have to go to Safari->Settings (used to be Preferences, I recall) and then Advanced, and check Show Develop menu in menu bar to enable this.
Sorry for the complexity, but things keep getting more complex, and Apple sometimes "almost hides" things.
Geniuses, you know.
Good luck.