SSAS error deploying project: Ensure that 'SQL Browser' service is running
i'm not sure to have a good view of what you are doing...
But i can say that SASS service is not included with sql server express. You can only have the reletional database service .\SQLEXPRESS, not the analytics database that is SSAS.
https://docs.microsoft.com/en-us/analysis-services/analysis-services-features-supported-by-the-editions-of-sql-server-2016?view=asallproducts-allversions
Instead of Express edition, download devenloper edition. It's free for not production env and full of features like enterprise edition. So you can test everything. Don't use it in production.
During sql dev setup be sure to select SASS instance too: