Is my way to change WordPress server is correct?

It would seem you have covered all your bases and your site is working as it should.

An additional step I have found useful is to verify hard coded paths within your exported SQL file because problems might not appear for weeks after the move.

I have moved a sites a few times and it seemed to be working fine, but after a few weeks I noticed some images were not appearing. My site had previously been http and I had moved to https for additional security. Some of the plugins used would save an image location into the database as http://example.com/wp-content/blahblah and that was incorrect.

If I ever move my site I always search the exported text, using a text editor, for http://example.com and replace with https://example.com. I also check if file paths have changed such as /doc/mydomain/public_html might because /var/sites/mydomain/public_html.

Having your site in text format gives you an opportunity to globally replace various things 🙂

That fixes any items hard coded by badly written plugins. It also takes care of the WordPress Home & URL items as mentioned by D.Dimitrov in the comments.

I hope this helps you and others who might stumble across this.

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