Based on the information you provided, I understand following. Is it right?
1.https://xxxxxxx.sharepoint.com is a communication site and home site in the tenant.
2.Search is a subsite under https://xxxxxxx.sharepoint.com.
In the communication site, you cannot enable Server Publishing Infrastructure feature in it.
And master page (HTML page) must have Server Publishing Infrastructure feature enabled.
So, by default, you cannot add master page (HTML page) into the communication site.
As a workaround, I suggest you use team site.
Sorry for wasting your time by not explaining this in the previous answer.
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