From your discription, did you mean that after you removed the app and added it again, you could not add the spfx web part?
In site contents page, can you see the app installed?
Besides, some spfx web part needs to enable custom script for you site. You could try to enable custom script on your site with the below command, check if it works for you.
Set-SPOsite <SiteURL> -DenyAddAndCustomizePages 0
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