In the Namecheap site, click Manage next to the domain you want to
verify with your Google service.
Click the Advanced DNS tab on the domain dashboard.
Scroll down and click Add New Record under the host records table.
Select TXT Record from the record type drop-down list.
Paste the entire verification record into the Value field.
Enter @ in the Host field.
Leave the TTL field set to Automatic.
Click the green check mark to save your TXT record.
Note: The change may take up to 24 hours to update. However, as you go
through the next steps in the Setup Wizard, the wizard immediately
starts checking for your new TXT record to verify your domain.
Can you try that? If it doesn't work, let me know and also reach out to support@firebase.com.
Your attached screens do not show your CNAME configuration. Even though firebase instructions indeed only asks for two TXT records, records that are both correctly set up as your screens show, I believe that these pair of TXT records that firebase requests do not free you up from the need of setting up at least a CNAME record in addition to both TXT records.
This was my case: while I did not set a CNAME record, firebase never recognized my domain.
I am not an expert (sorry!), but in the lack of other answers, even I may be helpful to suggest that you set up your CNAME record to point to:
CNAME record
host: www
value: [yourfirebaseappname].firebaseapp.com.
(Please note the dot after the '.com').
In my case this was enough to make firebase works well and recognize my domain.
In my specific case, and I'll register here at least for my own future use, I prefered to use, as an after step, both A records supplied from firebase as my way to route to my domain without www.
I believe this can be done with CNAME, but in my case the final setup was:
Advanced DNS Management
type: CNAME record
host: www
value: [my-domain-name-without-www]
type: A record
host: @
value: [IP address from firebase, like '1.2.3.4']
type: A record
host: @
value: [Second IP address from firebase, like '2.3.4.5']
Everything is working fine using this configuration. Goal reached.
As a todo future step, It would be useful to learn how to achieve similar goal using the CNAME record pointing to firebase domain instead of A records pointing to firebase supplied IP addresses.
I had issues connecting my custom domain as well, apart from using @ in the host field and the CNAME, you'd also need A records. Here's all I ended up with, I sat back a while for the domain to get propagated (I had just purchased it) and waited for 10 minutes after adding all of the records and it worked. Also I've found helpful instructions in this blog post.
I was having the same issue for days (my custom domain made it through the verification stage but would not connect) but it turns out that I didn't have to change my DNS configuration to fix it (the screenshot for the config that worked is below for reference).