No. Not since 2014.
That rule was real in HTML4, where one H1 anchored the document. HTML5 introduced sectioning elements — <article>, <section> — each of which can carry its own H1. Google's John Mueller has said outright, on camera, that multiple H1s are fine and the site "will be ranked normally."
What actually happens when you panic-merge everything into a single H1: nothing good. You contort a clean heading structure to satisfy a guideline that stopped applying a decade ago.
The thing that actually matters is hierarchy — that your headings describe content in a sensible nested order, so a screen reader and a crawler can both follow the outline. One H1 or three, the question is whether the structure makes sense.
(The auditing tool flagging your "multiple H1" error is older than the spec it's enforcing.)
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"You can only have one H1 per page."
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