How can I allow my wordpress site to accept both Basic Auth and Oauth 2.0 via bearer token?

I can fetch entries using Bearer token from one my of my apps if the .htaccess file has the following lines in that specific order:

But if I try to access it via cURL, using Basic Auth, I get:

Now to avoid that, when I go back to .htaccess file and reverse the positions of the lines above, so that the first one comes last, and last first – the basic auth request works well and returns resources requested, but at the same time, the other app that users Bearer token doesnt work:

I’ve been going over this almost all day. Please help. Thanks! (NB: I really need to be able to authorise with both Basic and Bearer token). Thanks!