You could try the free version or the PRO version of duplicator.
https://www.ads-software.com/plugins/duplicator/
I’ve used several different (paid) packages including the one you mentioned and Duplicator is hands down the “most reliable” in my experience. I’ve used both free and paid versions dozens and dozens of times to backup, migrate to new domains, migrate to same domain but different host.
It takes less technical skill to use Duplicator that Updraft.
Here they list the hosting platforms on which it definitely works (has been tested)
https://snapcreek.com/duplicator/docs/faqs-tech?utm_source=duplicator_free&utm_medium=wp_org&utm_content=free_disclaimer&utm_campaign=duplicator_free#faq-hosts
….but I’ve used it on other platforms with no hitch including self-hosted Ubuntu, Linux and Windows servers (running Apache, Nginx, IIS, MySQL, MariaDB).
The only time I have encountered a problem is migrating from one host to another (it is usually a MySQL incompatibililty) but Duplicator support is very good…even for the free version.
The PRO version is not that expensive and well worth the “automated” backup features which you could (should) use once you get your site migrated.
Whatever you do, make sure you get the migration done before the old version is destroyed. Also check to see what version of WordPress, MySQL, PHP your old version is currently running on … useful for support to help you resolve problems. This plugin, for example, will display all that information for you.
https://www.ads-software.com/plugins/version-info/
If you try duplicator and have any questions, I will respond. (I have no affiliation with Duplicator…I am just a user).