[Need advice] does my Seo rank will change ?

Hi I'm currently working on developing a store using WooCommerce for a client and this client already using his website but was developed with a company and they also used wordpress but they share with the clients different platform so the client don't have access to the actual wordpress panel,

So my question is after i develop the website and setup everything i will point the original domain name on this new "server/host" does the Seo rank will change!? and i already kept all the link the same so all the links on Google will point to the same article just different design and different server

There will be flux in the ranking but keep in mind to not change any URL of any page and keep in mind the on-page.It will be back on track on some time.

okay thank you ) and for pictures too?? like at the moment the pictures are .jpg but in website i developed it will be .webp for better results