Solving 'WP-CLI Updates Not Found'

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That's one (slightly annoying) problem solved - I've managed to upgrade the WordPress version and plugins on https://abulman.co.uk/ on the second attempt.
I use WP-CLI to do it all from the command line (and then commit all the changes into Git), but when I last tried to update, it had been reporting that everything was already up to date - even though the dashboard was lit up like an Xmas tree with new version notifications.
1$ wp core check-update
2Success: WordPress is at the latest version.
3$ wp theme update --all --dry-run
4No theme updates available.
5$ wp plugin update --all --dry-run
6No plugin updates available.
If the issue was a caching plugin - turn it off for a little while....
Initially, I forced a version update with wp core update --version=6.9 --force, but wanted to find the general solution. Searching found a couple of posts saying that security or caching plugins could be the issue, so I ended up making a quick edit in the W3TC drop-in plugin file at wp-content/object-cache.php, just adding a return; at the top so it wasn't used. That solved it, and I could upgrade all the themes and plugins, before removing the line again.
As that WordPress site is the only thing I've got on the server, I'll take another look around for a good looking theme for Hugo to replace it with a Github pages version and setup all the redirects in LuaDNS to send them there. Or maybe I can just add some things to my Github front-page at https://github.com/alister instead? I'll have a think and see what I can do.