Nextcloud, Qbittorrent, Truenas and loads of other svcs take optional email credentials for sending alerts and other features (eg. password recovery for nextcloud).
What email providers do people usually use to make this process simple to set up? For example, Microsoft doesn’t allow basic auth anymore so it’s supposedly not possible to use via most of these setups, and some other services seem like they have a low inbox size (does this matter?)
You only need SMTP server, so the inbox size doesn’t matter (assuming you have another email where you want to receive those notifications). And even if you have separate inbox for alerts it’s quite unlikely that you get hundreds of megabytes worth of alerts every day and they’re pretty much useless after a day or two so there’s no need to keep them around.
In here ISPs commonly have SMTP service included on their service, so that’s worth checking. Beyond than that, any at least somewhat reputable provider will do as long as they provide traditional SMTP service. One option is to use a relay host on local network which sends mail trough a smart host so you can just use local unauthenticated SMTP server for all the things you run and that one service will then push the messages to the internet.