How to properly setup routing in vue-router with few optional parameters, decent url and automatic link generation?

Question

Vue.js

Hello.
The task is to make routing in vue-router subject to the following conditions:
1. some parts of the url must be passed as props to the vue component. eg /test/page/3/pagesize/30 or /test?page=3&pagesize=30 or /test/page-3/pagesize-30
2. all parameters are optional, ie. some parameter may be missing in the url, and this props in the vue component will take the default value, and most importantly, the router will understand which route is meant.
3. links in the router-link component containing a link to itself and one parameter should automatically pull up the rest of the props that are matched with the route.
I partially managed to solve this problem: https://codepen.io/Razbezhkin/pen/JjjPjQO?editors=1010
but in my case it is not possible to make it so that some parameters in the url do not need to be specified.
and the appearance of the url is somehow not very pleasing to the eye.
Tell me, how do you solve such problems?
Thanks

Answer 1

No need to produce questions. In general, something like this:
https://jsfiddle.net/23s4czfa/1/
added for paragraph 3
https://jsfiddle.net/nsr54z7c/