1000+ channels sounds insane. Maybe it's normal to use Slack like that in larger enterprises, but IMO at that kind of scale they need to have separate Slack workspaces for each team, and then higher level ones (or a different method of communication) for higher-level strategic & executive planning. Even if you're not expected to be in the vast majority of them, having 1000+ Slack channels all under one workspace would be overwhelming for a lot of people, I'd think.
For the OP trying to manage that situation, I'd say leave or mute any channel you don't need to be in, set it to only notify you for @ mentions. (@channel mentions would depend whether it's abused; if not, those could be included too. If it is, then probably best not to notify on those.) And then yeah, as you suggested, aside from people specifically tagging or DMing you, only look a couple times a day, at specific times.
If you think that could cause inconvenience for others, or if even just the @mentions are too much, it could be worth bringing it up with your manager too. (If you've got a good manager, probably worth bringing it up regardless.) Try to approach it not as a complaint, nor as something you can't handle, but just a challenge to be solved, like any of the many engineering challenges you work through every day. Along the lines of, "Hey, I was wondering if I could run something by you. I've noticed that with all the Slack channels we're in, I'm getting pinged pretty regularly. I want to make sure I'm available when people need me, but I also find it helpful if I can have uninterrupted stretches to concentrate on coding. Was thinking a decent solution might be ______. What do you think?" Of course you know your manager better than I do, so obviously tailor it to how you'd normally communicate with them. Personally though, I always appreciate it when someone on my team comes to me with an issue in that way, as an opportunity for improvement. They might even have some useful ideas, or be able to help facilitate.