It's an aspect of the dryer design. Some are more apt to accumulate some lint residue in areas outside the filter.

You could try adding some adhesive insulation strips around the door gasket area shown in your second and third photos .... but too much added thickness vs. what's native to the machine will prevent the door from closing securely and potentially popping open during operation. Alternatively is replace/refresh what's there with the manufacturer's part.

Same for the strip that's askew in the filter slot but the risk of adding something non-spec there is if it loosens and get sucked into the blower.

Is there an actual lint screen for the slot? OP did not mention it. Could that be why there is lint accumulating everywhere?

Thank you both for taking the time to respond and share your thoughts.

@armjim - Yes, there is a lint screen for the slot, which I've included photos of below (and should have included in my original post). There's no hole or damage to this part, as far as I can tell.

@dadoes - do you know what the precise name for that part would be? Its some kind of foam (definitely not felt), and when I've tried searching online (like here: https://www.repairclinic.com/ProductDetail/618823) I cannot find anything matching the description.

My other thought would be to get some high temp adhesive and just re-attach the foam in place. Would that seem viable?

Parts illustrations captured from an online source (SearsParts). All the relevant items are tagged as NLA from GE (although may be available via eBay as used or new old-stock, or 3rd-party items via Amazon).

The filter housing/air duct 1302 fits to the slot for the filter in the front panel 1222, and presses against the hole in the face of 1310 the front of the blower housing.

1301 may be the gasket that's torn, which seals against the filter slot in the front panel 1222.

1302 is described as a plug or push-in fastener, appears to be six involved per the holes illustrated on 1302, perhaps anchors 1302 to 1222.

1301 = P/N WE09X10001 Air Duct Seal

1302 = P/N WE01X1262 Plug or Push-In Fastener

1306 = P/N WE14X10050 Air Duct Assembly

Adhesive to attach the torn gasket could be done ... but that may not do much to solve your lint residue complaint. The blower pulls air through the heating element and perforations at back of the drum, through the perforations of the inner door panel, down through the filter and blows out the dryer's exhaust ducting.

Does it take a long time for your clothes to dry? I'm wondering if your dryer vent might be clogged, so there isn't a lot of air flow through the lint trap.

@dadoes - Thank you for the follow-up. It turns out I was looking at the wrong diagram to find the part I was looking for. I take your point that it probably isn't the root cause to what I'm seeing.

@AnnKH & @3onthetree - Thank you both for your input. Based on your comments and dadoes' explanation, the dryer vent does seem relevant. While I haven't noticed issues with my clothes being damp, the build-up of lint around the door perimeter seems consistent.

I won't be able to fully investigate this immediately, but appreciate your guidance. The part of the part of the flexible hose I'm able to access from the front of the machine seemed clear of blockages - I'm not able to access the back of my washer/dryer easily, so will need to check the rest of the hose this weekend. I live in a condo building, and the dryer vent connects into an internal wall, so I'll need to do more investigation on the termination cap and what can be done.

There are alarming videos on YouTube from services that specialize in cleaning dryer exhaust ducts.

We had ours cleaned last summer - it was a new to us house, and I never thought to ask the previous owner when he last had it cleaned.

It was pretty nasty - LOTS of lint! Our laundry room is not on an outside wall, so there is a lot of duct to fill up.

Now it's on my calendar to do it every other year.

Easiest to fix and most likely is a clogged duct.