Hello Elowy Groot,
Thank you for contacting Dynamics community.
Regarding your question I had tested the scenario and I am able to see the email over here:

To clarify what I've done:
Other than setting the regarding to the abc account and creating the email from the custom entity, I've also enable those options for the source entity, in your case the Shop:

The three of them are not mandatory as the first and second one will enable you to link the custom entity with note and email and you should only enable them while trying to create a custom relationship or let the system create a relationship with the two of them.
The third one is not mandatory either, but as I worked with an email, that one is good to have for now.
Please verify if you have it in the Activities tab instead of the one you had been looking into, this time around for the account form.
Regarding the timeline itself, most precisely the social pane, this one here:

The Post view is controlled, as far as I remember, by the Activity Feeds SDKs, those over here:

Which means those will only be updated in case the message on SDK Message column will be performed on the entity on the Primary Object Type code and we do not have them for all entities.
Could you please verify if the email you mentioned is part of the Account Activities view?

Thank you!