Is the macOS recovery also upgraded when i run mac upgrades?
When you restore a Mac from Internet Recovery it restores the OS version that came with the Mac when it shipped. So if your Mac came with Mavericks than it will reinstall Mavericks. From there you can then reinstall Mojave right over top of the new Mavericks installation.

It will not install beta OS versions as there must be an OS in place with the necessary macOSPublicBetaAccessUtility installed.

As for the recovery partition OS version, I am unsure of what happens to that during major macOS upgrades. I would think that it would not change as Internet Recovery works even with the recovery partition deleted. Which tells me that Internet Recovery is (at least mostly) built into the firmware of your Mac.

Correcting During an OS upgrade recovery is upgraded as well so you will get the latest (non beta) version of macOS. Thanks to @Tetsujin and the OP.

Going back a revision or two and then upgrading from there works perfectly well, it just takes longer. For that reason I always make a bootable USB installer of the last two versions of macOS and keep them in a drawer for eventualities such as these. 8GB flash drives are cheap and it takes little time to create a bootable macOS installer. Perhaps something to consider for the future.