The fact emails Alice sends to other users, which are then forwarded to this user, are also deleted - stinks of an inbox rule to me.
First some stupid/ back-to-basics questions - you said the user only uses web and mobile, but you also referenced rules in Outlook - they aren't always the same. I'd start by using the web only. What happens if you search the inbox for [email protected] is the new (disappeared) email found? Are any emails from Alice found? Did you specifically check for inbox rules on OWA? I'd be surprised if o365 support didn't check these but - you know - gotta ask.
Change your user's password and initiate a sign-out, in case another client eg outlook is running somewhere.
Did you check transport rules aka mail flew rules? Slightly long shot but possible I suppose.
https://learn.microsoft.com/en-us/exchange/security-and-compliance/mail-flow-rules/mail-flow-rules
I agree with the message trace idea, though it may only show as delivered, it might also tell you where it went afterwards. Don't get the farm on it giving you the answer.
If it's not affecting other users in the company i.e. emails from Alice arrive OK then it does suggest it's related to your user. I'd say look at your AV if you were using outlook desktop, but you said the user doesn't use outlook desktop?
Disconnect the mobile client for a short time to confirm but I don't remember there being anything on a mobile client that could do this, it's worth eliminating it.