Does it matter if the very first user, usually Admin, does not have a user ID of 1?

No.

If the plugin relied on it, it was badly written – if I found such a plugin, I would delete it instantly because you can’t know which other mistakes the authors made.

Actually, plugins shouldn’t care about the ID at all, but about the user’s roles and capabilities. In the end, IDs are only needed because it makes it easier for the database.

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