Hi @jellybean and welcome!
It’s nice to see you planning things out and you’re definitely asking all the right questions.
RankMath will be fine, @gulshan here is at least one I know using it without issues now (on version 6.6.21 of Static HTML Output plugin).
GTM and other embeddables (including Hubspot) should have no issues. Animations should all be fine, if they are CSS/JS based, not requiring any calls to the database once page is rendered.
Insert Headers Footers should be fine, I’ve only used HFCM plugin, which I assume is identical in functionality.
Not sure what WP Optimize is, but let me know if any issues pop up.
Now, the important parts, setting up your hosting:
dev.mydomain.com (can be on siteground, should be non-public, ie http basic auth login/password to stop bots/attacks on your dev site)
mydomain.com - the live site, hosted on Netlify, Cloudflare, Vercel, S3 + CloudFront or any other static site host
You can also opt to not keep any SiteGround/remote hosting account active, if it’s only you working on the dev sites. You can then run them on your own local computer and just publish the static site to Netlify/remote host.
So, the first step, is to choose local or non-public subdomain (please avoid subdirectory WordPress installs, not really supported and causes more issues than worth) then clone your current live site to this new “dev” server.
From here, you can do a test deployment to a new throwaway Netlify site, like mytest1234.netlify.app (set this in plugin’s Deployment URL setting), export a zip and drag and drop into Netlify.
Check the site loads fine in https://mytest1234.netlify.app - make sure no insecure content, 404s or console errors, maybe run some speed tests and adjust
_headers file in Netlify to improve caching, add any existing redirects if needed in
If that all looks good and you’re confident, then you can change your deploy URL in the plugin, create another new site in Netlify, this time, setting your
mydomain.com in Netlify and changing DNS over to Netlify, as per their instructions, wait for DNS changes to propogate and you should be looking at your faster, secure site at https://mydomain.com via Netlify/other host.
You then keep working on your dev site, be it local or on SiteGround/other host (see note below), retire the old production hosting account and just redeploy when you make changes to the site.
If you are making a lot of design changes/adding plugins, etc, I’d recommend to also incorporate a “staging” environment, which can just be another Netlify site (they’re free!) and do a quality check there before updating your live site. Also useful if you’re doing client work and want to send them specific snapshots of a site, you can deploy to as many Netlify staging sites as you like and just send them the link.
I’m sure you’ll be fine once you’ve got a cpl static site conversions under your belt, but you may encounter issues initially, which is normal - just post any questions here on the forum and myself or others should be able to guide (and later improvements to the plugin/documentation should make things easier for future newcomers!).
(I’m not a fan of SiteGround for many reasons, so if you have opportunity to stop paying them for any more hosting, I’ll happily recommend you some more professional VPS options)