That's interesting, haven't heard that combination of circumstances before!
Instead of muting the account, you could try putting it on a "List" using Mastodon's Lists feature. These optionally let you hide the account's posts from your main timeline, so that the posts only appear on the list. It shouldn't affect notifications.
More info about how to use Lists at https://fedi.tips/how-to-use-the-lists-feature-on-mastodon/

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