Hi Steve,
This is one of the issues why the old “section” module was obsoleted. It’s simply a pain to deal with as it is old technology.
But to help you out:
Plugins like Raw HTML generally should be the answer to this. But you’ve already mentioned that you’ve tried plugins and it didn’t work, I’m not sure if anyone is still developing for this knowing Classic editor itself is obsolete as well. WordPress isn’t even planning to support if anymore as it’s end of life is on December 31, 2021.
If I may suggest, try changing to the Block editor and just do parts that require HTML on a Custom HTML block.
Note: The theme doesn’t control this. It’s a WordPress core function.