Hi,
We have a custom module will help send emails through SendGrid Mailing Service, Please check whether it meet your requirement

Here is the link to the app:
https://apps.odoo.com/apps/modules/15.0/sendgrid_email/

Hope it helps

you can check the following sections:

1. Verify API Key: Ensure that you have entered the correct API key provided by SendGrid. The API key should have sufficient permissions to send emails.

2. SMTP User name: Set the "SMTP User name" field to "apikey" as you mentioned.

3. From Filter: In the "From Filter" field, you should specify the email address from which you want to send emails. Make sure you enter a valid email address associated with your SendGrid account.

4. Sender Email Address: Check the email address associated with the user sending the email. Odoo uses the user's email address as the sender by default. Ensure that the user's email address is valid and matches the "From Filter" value or the configured SendGrid sender email address.

5. Outgoing Mail Server Configuration: Double-check the configuration of the outgoing mail server in Odoo. Make sure you have entered the correct SMTP server, port, SSL/TLS settings, and authentication details (SMTP User name and Password, or API Key in this case).

6. Test Connection: Use the "Test Connection" button in the outgoing mail server configuration to verify the connectivity to the SendGrid server. It will help you identify any connection or authentication issues.

7. Email Templates: If you are sending emails from automated actions or workflows, ensure that the email templates used in those actions are correctly configured. Verify the sender email address and the template content.

8. Error Logs: Check the error logs in Odoo for any specific error messages related to email sending. You can find the logs in the "Settings" menu under "Technical" -> "Logging" -> "Error Log".