Some hosts will carry out the site migration for you for free.
I left Siteground some years ago for the same reason you are now looking elsewhere.
I currently use Ethernet Servers hosting - https://www.ethernetservers.com/
They offer free site migration and are also relatively cheap.
You can also choose to host your website on a server in the UK or France depending on where most of your traffic comes from.
It might also be a good idea to consider moving your domain name to somewhere like Namecheap. That way your domain name and hosting are separate and you can easily swap and change services in the future.
I have been using Namecheap for years because they have consistently good pricing for domains and renewals usually around £8 or £9 per year depending on what you choose.
You can also get some money off when you buy or renew a domain if you have the Honey app installed in your web browser, it will automatically search for and apply any available discount codes.