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It would seem logical to refer to the group by its URL rather than its
posting address,

Yes, and Mark was called on this recently in beta. I think it was the formatted Digest where the text of a link was the group's posting address but the URL under it was its home page. It did the "right" thing, but some felt it was confusing.

Agreed, needless ambiguity is definitely confusing.

unless a group permits non-subscribers to post, clicking on the
posting address shouldn’t take anyone to the group website…

In the invitation those were not links, so they wouldn't take one anywhere.

Unless your email interface linkified them (some interfaces will recognize an email address in a message body and make it clickable), but that would generate a message to that address, not take you to any site.

Thunderbird will linkify email addresses, but only in plain-text message bodies, Gmail doesn't. Possibly your email interface does in both plain text and formatted message bodies.

| You have been invited by <me> to join the Groups.io group <groupname>@groups.io.
Outlook.com did make <groupname>@groups.io into a clickable link for /g/<groupname>
Again why be confusing by needlessly mislabeling an address (a URL as an email address)?

... I would think it is more likely that a new subscribe would rather
go to the group upon joining rather than immediately sending a message
to the group.

True, which is why the only link in the invitation itself is the acceptance link. Which only takes you to the site (probably to your subscription page in the group, but I don't remember for certain);

It actually took me to the group webpage where I was already signed in with a different email address

it does not also open a new message either on site or in your email interface..

Yes, it didn’t, but it looked like it should.

Groups.io should strive to be clear and simple to understand and use.
It is misguided laziness to forsake simple corrections because 'those in the know’ understand that mislabeled items don’t mean what they look like. At best that generates confusion the rest of us have to deal with.