In this kind of thing you just go full on formal by requiring the request via e-mail, were you notify them that you're not qualified to do it and require confirmation (and, if applicable, confirmation that your own manager authorizes it).
(Also if you are busy with some other project, be very very explicit it will have to be put on hold and request confirmation that the manager in charge of that project has authorized it).
By this point, in all likelihood the person doing the request will give up. If not and you do get a go ahead, you're now fully covered to take tons of time, do a bad job of it and it's will officially be the fault of the person who asked you to do it.
I have ended up in this situation! The first commenter is extremely right. Realistically, your manager doesn't want you wasting time on a "learning opportunity". They need you doing what you're good at
By this point, in all likelihood the person doing the request will give up.
I have found in a majority of cases, they don't even remember requesting it. I give those requests the scream test: don't do it and see if they even notice. Sometimes they do, depending on the management, but most jobs like the OP cartoon just say stuff to look important in the moment and have zero follow up plans to make sure it was done.
Say outside of my familiarity as it's not my skill set.
Suggest bringing it to a designer
If they push for it, elevate it to a higher up. Your boss is paying you to code, not to Photoshop. And if they're so stupid to not defend you, you have bigger problems.
Launch an entire design movement among developers, developer-managers, and PM that runs in the face of every good idea from design with horrible consequences.
I deal with stuff like this on a daily basis as I'm in a hybrid function in support / sys admin. We get this not from managers, but from our users. "Hei this is how we would like to work, can you please change the system?"
While I absolutely understand the reason for this, it's hard to do for 600 users. And our new boss also supports this approach because we need to be a good service provider for our internal customers. But always having to research if the requests even are implementable and what the implications of the implementation are is so fucking time consuming. I still have other shit to do.
What I want to say is, I feel like I shouldn't always have to be the one to directly receive (change) requests but they should already have been checked and approved.
I shouldn't have to do 1. & 2. or even 3. from your list. I should receive a clear work order and then look into the implementation.
Ignorant supervisors (and judging by the comments here, many engineers) who think that engineers can do a graphic designer's job with no graphic design experience are the reason why so many corporate logos, websites, email templates, official apps, apps in general, and branding in general just look ugly. But they don't care because somehow a prerequisite for becoming an engineer or someone who supervises engineers is a complete lack of any kind of aesthetic sensibility.