If you mean that a microservices architecture for your back-end (e.g. running on a kubernetes cluster): yes. Any of the modern front-end frameworks can work. It is more importantly that you create a good API gateway on top of your microservices, to ensure your front-end talks to one service (the API gateway) only. This has different advantages, like: good user access control on API level, ensure certain services cannot be touched by the front-end, create API calls specifically for your front-end (e.g. Best-For-Front-end structure with GraphQL) just to name a few. With a good API gateway on top of your microservices, it should not matter if you use React, Vue, Svelte or any other framework.
I find the architecture I describe especially working well when used on top of big applications consisting of a solid front-end, a highly available API gateway, and a microservices application as a back-end.
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Would you suggest VueJS for the application that is based on microservices?
If you mean that a microservices architecture for your back-end (e.g. running on a kubernetes cluster): yes. Any of the modern front-end frameworks can work. It is more importantly that you create a good API gateway on top of your microservices, to ensure your front-end talks to one service (the API gateway) only. This has different advantages, like: good user access control on API level, ensure certain services cannot be touched by the front-end, create API calls specifically for your front-end (e.g. Best-For-Front-end structure with GraphQL) just to name a few. With a good API gateway on top of your microservices, it should not matter if you use React, Vue, Svelte or any other framework.
I find the architecture I describe especially working well when used on top of big applications consisting of a solid front-end, a highly available API gateway, and a microservices application as a back-end.