Recipients are not receiving my emails

You have not set up an Apple ID and a web mail account using like gmail , yahoo services , as in the location system preferences > iCloud Apple ID is signed in , that's the reason there is no web mail account enabled and not showing with connection doctor , try to set it up .

And see this paragraph from apple help .

If you’re having trouble receiving email with iCloud Mail, try the following:

• Make sure you haven’t turned on email forwarding. If email forwarding is turned on, messages you receive might be going to a different account. To check, click the Action pop-up menu in the sidebar, choose Preferences, then make sure “Forward my email to” isn’t selected. If you deselect it, make sure to click Done.
• Make sure you’re using a browser recommended in the Apple Support article System requirements for iCloud.
• If you’re not seeing email from a particular sender, check your iCloud Mail rulesto make sure you don’t have a rule set up to delete messages from that sender.
• Check the Junk folder for messages that were incorrectly marked as junk.

Read these articles https://support.apple.com/en-in/HT204230

Recommended system requirements

iCloud1 requires an Apple ID, an active Internet connection, and up to date software. If you meet the recommended system requirements below, you can take advantage of the latest iCloud features and get the best overall experience.

See this also https://support.apple.com/en-gb/HT203528

https://support.apple.com/en-in/HT204316

https://support.google.com/mail/answer/56256?hl=en

https://support.apple.com/en-in/HT208682

A web mail account configured with IMAP accounts always work , I don't know why you are avoiding installing it .

These articles are for recipients https://support.apple.com/en-in/HT204075

Also for the time being create a new test user account see this article https://support.apple.com/en-in/HT204443

And then configure mail account https://support.apple.com/en-in/guide/mail/set-up-mail-with-your-email-accounts-mail35803/mac

You can send a feedback https://www.apple.com/feedback/icloud.html

But this is a special case for your Mac that mails are not received , either the mails are going to their junk mail boxes or what ever settings they have done settings in mail preferences , also you said in your original question that if you try to send a mail to yourself it won't come to inbox , so the conclusion is erase the hard drive and reinstall Mac OS https://support.apple.com/en-in/HT204904

If there was a fault in outgoing server settings then connection doctor must have shown red dot in front of SMTP and it is showing green as you posted in your screen shot , either you are attaching large mail attachments or mail sending limits is over .See this https://support.apple.com/en-in/HT204208

These are some articles https://support.apple.com/en-in/guide/mail/outgoing-server-settings-cpmlprefsmtpserver/mac

https://support.apple.com/mail-settings-lookup

https://support.apple.com/en-in/HT204208

The third article is most important as the Mac user has never to set up port settings or other settings manually , once the account is configured the settings will get set by own .

What i thought is if the mail application get corrupted there could be many reasons , either some anti virus , third party softwares , unidentified applications are used or the system files are corrupted so the better way is to reinstall os , but as you said that the web iCloud mail account is also not working , so check out the port settings , I don't know about your service provider details , as around the world there are many service providers and no one can guess there port settings / either you are using VPN services , a fault incorrect connections in routers , slow network speed etc .

In your system preferences > internet accounts can you see both web mail account ( like gmail ) and iCloud account or do you have clicked on subtract sign and removed it ?

Also see this screen shot in system preferences > iCloud the Apple ID is signed in , the Apple ID address is kept same as gmail address , and all the boxes for mail , safari .....are checked in .

I am having a web mail account configured with an IMAP account + iCloud account and never faced this issue , if it had been I would straight away erase the hard drive and reinstall os and don't search for other solutions .