Linux Travel Laptop (<1.8kg, €1000-1500): Should I go eGPU or Built-in dGPU for Gaming?

[TL;DR: Need a travel laptop (<1.8kg, USB-C charging, Linux-ready, 13-16", 16GB+ RAM) for €1000-1500. I want to game at home via eGPU (TB5/Oculink), but those ports are rare/expensive. Should I get a laptop with a built-in dGPU instead, or just buy a cheap ultrabook + build a desktop? Framework 16 is too heavy, Framework 13 lacks the port. Help!]

I feel like I'm asking for the impossible with what I currently want, especially in these times.

I currently have the Acer Aspire 5 A515-54G (i5-10210U, MX350, 8GB RAM, 1.9kg, 1.8mm thick).

What I absolutely need:

• USB-C Charging
• Full Linux compatibility
• Screen: Between 13" (preferably 14") and 16".
• Weight: At most 1.9kg.
• RAM: At least 16GB (preferably 24GB+, but I'm willing to upgrade later)
• Longevity: Needs to be future-proof; I don't want to replace it in 3 or 4 years.

Budget: $1620 / 1500€
Country: Germany / EU

And now to the "impossible" part: I would like to game on it as well. When I'm traveling, I don't need gaming capability, so I thought an eGPU would be perfect. I was hoping for Thunderbolt 5 / USB4 v2 or an Oculink / TGX connector. But then I realized those are either not really available or are crazy expensive.

What kind of Tasks/ Gaming do I do?

• During Travel: Not much. Maybe some retro gaming/older titles (pre-2012), light emulation. I usually do browsing and Office work. I sometimes do some lightweight video editing on the go, but I think an iGPU should handle all of that just fine.
• At Home: I don't play that often anymore, so I don't need a NASA machine, but I would like to play modern games (eventually GTA 6 maybe) and do more demanding emulation (Switch, PS3, Xbox).

Maybe there is a laptop that fits my criteria perfectly, and I really hope there is one.

I've also considered Framework Laptops. The Laptop 16 is going to get an Oculink expansion, which would be great, but it seems heavier than my current laptop. The Laptop 13 would be ideal, but sadly there's no TB5 or Oculink connector planned.

With all this focus on eGPU during my research, I came to a question: If laptops with a good eGPU connection (64Gbps) are so damn expensive, wouldn't it be cheaper just to get a laptop that fits my needs but already has a dedicated GPU inside? Or might it even be a good idea to get a laptop fitting my needs (minus the gaming capability) for much cheaper and just build a Desktop PC (similar to how I lived the past years until my PC broke)?

If anyone has good solutions to this, it would be amazing. Thank you already! ^^