This has happened to us a couple of times, and we were able to resolve it by submitting a support ticket to Odoo. They gradually increased our email limit. In the most recent ticket, we received the following response from Odoo Support:

Thank you for contacting Odoo Support. 

I understand that you would like an increase in your daily email limit. Currently, your limit is set to 250. I would like to inform you that we have increased your daily email limit to 500. Please keep in mind that the daily limit will only be increased in increments in order to protect other customers who share the email server.

Before increasing your quota, we verify the following points:

• Your bounce rate for mass mailing should be less than 5%.
• Your emails must have an unsubscribe link.
• The email content must be relevant to your business activity.
• The recipients' email addresses must not have duplicates.

For any upcoming mailings, please remember to add an Unsubscribe link, as this may affect your eligibility for email limit increases in the future.

Unsubscribe: https://www.odoo.com/documentation/16.0/applications/marketing/email_marketing/unsubscriptions.html

We will consider increasing your daily limit only after you show a good track record of deliverability, which means a low spam rate, low bounce rate, and low unsubscribe rate over a period of time. If you require a further increase in your daily limit in the future, please create a new ticket for evaluation.

Alternatively, you can use an external email server to send emails from your Odoo database without any limit restrictions by Odoo. You can find the documentation on how to configure this here: https://www.odoo.com/documentation/latest/applications/general/email_communication/email_servers.html

Another suggestion is to have your users handle their notifications via Odoo, which will free up your email limit for communication with customers rather than internal notifications.

I await your response. As always, I am here if you have any further questions or concerns regarding this matter.

Hope this helps!