Um, no. That isn't sharing it. That isn't even having users run it. It's just letting others use it via the network.
It's Freedom Zero because you certainly have the freedom to use it, along with a lot of other freedoms. But you have to adopt the license for the code it touches if you involve others in your Freedom Zero use of it.
I think 99% of usage of the acronym FUD is dumb, so I don't use this lightly, but this is some pretty seriously bad FUD.
If you connect to your database using an AGPL licensed db client, you don't have to change all your codebases to AGPL. Unless your code is a modification to the tool, and you are going to distribute it to others, it imposes no obligations whatsoever. It wouldn't even make logical sense. If you write a new browser or even a curl replacement and license it AGPL, and use it to curl Google, would G have to AGPL their entire giant monorepo?
Both my comment (code it touches) and the comment I replied to (sharing the fork) were about this case. Nowhere did I say there was any reason to worry about it if it wasn’t the case, or that it was the most common case. I imagined integrating a browser based SQL client into an enterprise app where you want to give users database access as a scenario where that part of the license might apply.
It's Freedom Zero because you certainly have the freedom to use it, along with a lot of other freedoms. But you have to adopt the license for the code it touches if you involve others in your Freedom Zero use of it.