https://bitcoincore.org ist the proper website for Bitcoin Core and genuine downloads for it. It looks like bitcoin.org isn't kept very up-to-date with respect to downloads anymore.
These are versions you missed out (see at
https://bitcoincore.org/en/releases/):
Bitcoin Core 23.0
Bitcoin Core 22.0
Bitcoin Core 0.21.2
Bitcoin Core 0.21.1
Bitcoin Core 0.21.0
Bitcoin Core 0.20.2
Bitcoin Core 0.20.1
Bitcoin Core 0.20.0
Bitcoin Core 0.19.1
Bitcoin Core 0.19.0.1
Bitcoin Core 0.18.1
You can update step-by-step, but it should work if you immediately update with Bitcoin Core 23.0. It won't need to re-download your blockchain data, it will be preserved. Always verify your downloads of Bitcoin Core properly!
To be sure, an immediate update with the most recent version of Bitcoin Core is OK, I'd recommend to read the release notes of all intermediate releases. If there are some changes to the database structures or so pointed out, you may want to update with such intermediate releases first.
Seriously, v0.18.0 and v0.18.1 were released in 2019, we're now in 2022. It might be better to check for new versions in shorter time frames.
That's great, thanks for the clarification. It's a bit confusing with the way the versions are numbered, for example they go from a version 0.21.2 (which is less than 1) all the way to a full-numbered 23 now. Just semantics I guess.