It's a chicken and egg problem - websites, etc don't want to enable IPv6 because clients have broken IPv6 implementations and that causes delays and issues, and clients have broken IPv6 implementations because the internet providers don't care to fix it because nobody uses it.

(Many computers THINK they have IPv6 connectivity when they do NOT and so if they see an AAAA record and try to connect to it, it can cause a delay while that fails. Most browsers are better at this now (they will try to connect to both and show whichever answers faster), but not all network things are browsers.)

In the past, one of the factors was SEO. A few years ago (in 2018, to be precise), the company I worked for tried enabling IPv6 on some of our websites, and observed some drop in Google ranking, that recovered when the IPv6 experiment was undone.

Sorry but this is just too anecdotal for me. There are so many factors that go into Google rankings and Google itself makes it pretty easy to discover any crawling or indexing issues on a website that it seems the root cause of the issue should have been discovered (if it was due to a crawl/index) and I doubt it was a properly working ipv6 setup (something broke somewhere on your company's end is what I'm getting at). Cloudflare uses ipv6 and I doubt all their customers websites were being penalized by Google

Well, it was just a stock Hetzner dedicated server. All that was added/removed is a DNS AAAA record pointing to the server's IPv6 address. We used IPv6 before in order to access LXC containers hosted on that server. If THAT counts as a broken setup (which I doubt, see below), then, sorry, I don't see how we could do better.

I have personally checked the result from my then-home connection (unfortunately, through he.net tunnel) and it worked, and it was properly logged by Apache. The CEO had native IPv6 on the phone, and it also worked for him, and, according to Apache logs, IPv6 was also used. I have also checked that the site was still accessible over IPv4. So I indeed don't know what went wrong.

On the other hand, I did not have access to Google webmaster console and had to trust the CEO that the SEO problem exists. It might have been a coincidence. And again, the SEO problem was in 2018, and is likely irrelevant today even if it really existed back then, that's why I said "in the past".

Having access to GSC is really a must for stuff like this. You can see exactly how Google sees your page and it's status (error fetching, not indexed, different canonical, etc etc)