How to simplify external acces on SharePoint Online site?

If the partner organisation is also using Office 365 you should share to their Office 365 ID rather than have them create a Microsoft Account. Yes, it is confusing and the naming doesn't help as most people think their Office 365 account is their "Microsoft" account. Microsoft 365 branding isn't going to improve this.

You could consider creating a Microsoft Account for each of the external users and sending them the credentials (securely) so at least they are ready to go and they don't have to do the setting up and accepting the link. Another possible simplification is to create an Office 365 Group as the basis of sharing which would help make sure you only had to set things up the once for each user. There's a good explanation of sharing on the ShareGate site. 

If using federated identities for your partners is a possibility, that might be worth considering, although probably complete overkill for the scenario you are talking about.