Is it possible to painlessly change the internal links of the site?

Question

Search Engine Optimization

There is a small website written in ASP.NET WebForms. The number of visitors is small, but copes with its task. When adding some functionality, it was decided not to make unnecessary crutches, but to rewrite everything anew, in ASP.NET MVC, at the same time learning a new technology. Everything is great, but one question torments:

• On the old site, links to products were like /products/products/%product_name%.html
  
• MVC also allows you to make beautiful links using routes, for example /produccts/%category%/%index%
  

If the addresses of the site pages change, how will the search engines "react" to this (Yandex is especially interested)? Will the pages be re-indexed in a more or less short time, or will they wait for new pages to be raised to higher positions in the SERP for a long time, like "from scratch"?
Perhaps the questions will seem extremely stupid, I understand SEO poorly, almost nothing.
Thanks in advance for your answers.
PS Probably, it is worth strangling the sense of beauty and making links similar to the old ones?

Answer 1

This update will be really painless if the links remain the same.
If you change - write in htaccess 301 redirect and that's it.
After 2-4 updates, everything will be as before. BUT given the fact that the promotion was not referential. If links to some pages were purchased, then the effect will go to 0 when links change

Answer 2

Yandex is doing all this for a long time and painfully, I would launch the second site during the reconstruction of the first one, but with today's indexing speed, it may well be indexed in 2-3 months))

Answer 3

Web pings of new posts and sitemaps to help.
For Google, you can use the feed with the updated parameter (sorting updates) - this is the recommendation of the engineers.
Tips and Tricks for XML Sitemaps and RSS/... .