A company promoting their own products on their own websites is far from being criminal. Amazon.com right now just showed a giant splash for buying an Echoshow on their home page.
Imagine your bank, alphabank has 80% of personal bank accounts and 70% of auto insurance. When you check your transactions, you see a notice: "you could save up to x% by switching to alphacar."
That's the premise behind antitrust (even though in practice, its 50 years behind the times). If you have dominant market share, things that are otherwise lawful^ aren't anymore.
^Antitrust stuff like anti-competitive behaviour isn't criminal regardless.
It would be anti-competitive in your hypothetical if your bank refused to make transactions to your auto insurance company because it was not the bank's insurance company.
Pop-ups in your bank portal are uncomfortable but are not anti-competitive.
