I am contemplating buying the physical version of the GOTY edition, question is, does it have any online requirement to install/play? Like for instance, do the DLC require a download or is everything on the disk and can be fully installed and played offline?

If it's the GOTY version, there won't be anything to download since it should have all the DLC. Depending on when the disk was stamped it may only be the 1.31 version, there was a ~640MB patch released a month or two after bumping the game up to 1.32. The fixes were never listed which means it was probably very minimal, the only note for it is adding language support for 'simplified chinese' .

There is no online component for the game at all, and doesn't require any internet connection to play.

Thanks but I am asking for someone who knows by experience. I could come to these conclusions by myself with the information with have about the digital version. But things could always be different for a retail release as they unfortunately often are, especially nowadays with all the hidden "services" and I don't want to waste a cent.
I've also read you can't get patches (warez aside) if you didn't register the game on GOG (I've read this about the original release), could eventually be the same for DLCs of the GOTY, I don't want to take any risk hence why I ask.

Goty have all dlc, you need only install and play, the only problem, you need to download latest patch , if it is not alreay patched, this mean you can make a free account and register at gog.com, download install the patch, and go offline and play, if need it....I liked to make an account to get digital all the freebies and to use last galaxy...