Leak into cab from driver / 3rd door.

If the driver door hinge pins/ bushings are worn & on their way out, that can/will affect the door's relationship/ alignment with the cab. That may (but probably not) have an impact on the 3rd door, as the strike/ latch plate for the driver's door is on it. More importantly are the strike plates at the bottom of the 3rd door (@ the sill of the cab & @ the cab ceiling) which may need adjustment, as they will affect the 3rd door relationship/ alignment with the cab. One initial way to check for alignment of the doors to each other and the cab is to carefully examine all of the gaps between them - all of them should be uniform and even along their respective lengths. Under the back corner of the cab is a mounting bolt with a flexible bushing, which if deteriorated, might cause the cab to sag, so check that as well.

Get the driver door pins & bushings replaced with OEM parts (as a minimum). I just had mine done, and factory parts are definitely still available, and avoid the cheap Dorman ones (they are junk). Based on the photo, it appears that the perimeter door seal may not be fully 'seated' up against the cab, where you have indicated the leak occurs - you might want to double check that. The gap between the door seal and the upper seal at that location appears to be greater than the gap at the driver door area.

I had them replaced at an autobody shop, as I wasn't fully equipped to do it myself at the time. In my case, it was worth it to have it done. It's not a hard DIY job, and probably the most challenging part is getting the spring replaced. But with the right (simple) spring compressor, not bad at all. The bushings are a press fit installation; drive the old ones out and seat the new ones. It's critical to make sure the door is properly supported and braced if you plan to leave it on. Some folks just remove the door to do the replacements, and then rehang it by lining up the hinge leaves & inserting the pins, secured with the retainer clips. If removing the door, it's best to have a 2nd person to help, as the door can be heavy and a bit unwieldly for one person, hence less chance of damage.

The full set of bushings (uppers & lowers), retainer clips, and pins for the driver's door and labor was about $105. It was nearly an even split for parts and labor. The parts were sourced from the Chevy dealer by the body shop, so there was undoubtedly some markup along the way. I'm sure the parts can be had for less if you plan on doing it yourself. I had seen the Dorman junk pins, and they were an immediate no for me. Their price alone ought to be enough to raise some warning flags.

Edit: If the vertical seal of the 3rd door is 'petrified' and in need of replacement, it's a good time to do it. But I'm not convinced how that could be the source of the leak you indicated in the top horizontal seal area (but, hey, I've been wrong before!). Have you tried the water test suggested in post #2 to help track down the point(s) of the leak? One would think that the seal and/or body area at the the leak point(s) would be visibly damp and/ or wet where the water is entering. Keep us posted.

Based on the close up photo, I would suspect that the driver's door top hinge pin (&/ or bushing) is shot and allowing the door to sag. It could be the lower one is failed or failing as well. They should get replaced as a full set in any case. That likely is not allowing the corner of the door to properly seat against the top horizontal seal, and may be the source of the leak. That's similar to the situation on my Sonoma ext. cab, but mine wasn't leaking. It was, however a wind noise issue at speed, plus the door latch was a bit low relative to the strike on the 3rd door when closing the door. It also appears that there is some paint scuffing at the top corner of the 3rd door, indicating repeated contact from the driver door corner. I'd get the pins & bushings replaced and see if that (along with the new seals) doesn't rectify the problem. Let us know how things go.

Edit: Here are the part numbers used on my '03 (according to the local Chevy dealer. If you are plan to DIY, I'd double check them for your specific truck to be safe, but I think these parts were used for multiple years on the 2nd gen. cabs. One door will need 2 each of the following. And note that the OEM pins had different O,D,'s at the top & bottom of the pin, hence the 2 bushing parts.
Hinge pins: 93356553
Bushing, lower (larger I,D.) 16632192
Bushing, upper (smaller I.D.) 16632193
Retainer clip 25640501