If your website ranks on page 2, does it even exist?

valuable answer needed

4rd+ page is a no man's land.
Even on 3rd page you can still get a click here and there.

Also it should not rank that deep for all keywords.

It has potential, it holds value for most cases for sure,
It depends on type/volume of traffic as well, and could be pushed to page 1 relatively easily to get that traffic

Now keep in mind I’m a cup is half full kinda person: page 2 does exist, but usually only for a tiny fraction of people who are passionate or looking for more precise answers instead of the usual fluff. The good news is page 2 is really close to page 1, so if you’ve got your ducks in a row with metas, schema, a solid post, and maybe a FAQ or some EEAT (real or fake ), you’re often just a few quality backlinks away from breaking through.

If you’re stuck on page 2 for a competitive keyword, you can still leverage it. Google’s already telling you the content is relevant so that’s your chance to branch to longer tail less competitive versions. Hit those with supporting posts or sections and you’ll often end up pulling more traffic from page 1 long-tails than you’d ever scrape from sitting in limbo on the fat head.
Example: being stuck on page 2 for house cat then switching the focus to big house cat to make it easier to hit while bringing real traffic , and if you’re selling something you’ll usually get a more targeted buyer pool too (so less BS and better conversions).

Yes, I targeted top 20. That's been the rule I have been following.
Not beyond page 2.

Yes, second page is also important. It doesn't mean you are dead or you are nowhere. It means you are still alive you just need a little boost to pop up in the first page. Now research your competitors to get there.

If you improve site authority, you can reach first page. It depends on the competition too. So, 2nd page results exist and they matter too.

Being on page 2 means searchers rarely see you, so without moving to page 1 your content brings almost no business value.

It will still hold some value and traffic.

Ranking on position 30-100 actually have some benefits. The traffic is much smaller, but from personal experience the hits you get generate much longer sessions. It seems that people searching for something beyond page one are really interested and engaged in the topic. If the user intent is satisfied they tend to stay much longer on the website, view multiple pages etc...so in the end quality almost beats quantity.

Page 2 traffic is tiny, but yes, it still exists and can grow with optimization.