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

LAPTOP QUESTIONNAIRE

• Country

Germany (and potentially other EU countries)

• Budget

€1000 - €1500 (approx. $1080 - $1620 USD)

• Are you open to refurbs/used options?

Yes

• Screen size

13" to 16"

• Weight limit

Maximum 1.8kg

• Purpose

Travel/Student work (Office, browsing, light video edeting) + Home Gaming (Modern titles & Emulation)

• Form factor

Standard/Clamshell

• Intended usage

Travel: Light browsing, Office work, lightweight video editing, Retro gaming (pre-2012), light emulation. Home: Modern gaming (eventually GTA 6), demanding emulation (Switch, PS3, Xbox). Software: Full Linux compatibility is a must.

• Desired battery life

4-6 hours or more

• Please list, in order of most important to least important, the priority between Size, Weight, Performance, Battery life

Weight, Size, Performance, Battery life

• Info/Requirements

Must Haves: USB-C Charging, Full Linux Compatibility, At least 16GB RAM (24+ would be better, but I'm willing to upgrade later).
The Dilemma: I was hoping for Thunderbolt 5/ USB4 v2, or Oculink/TGX for an eGPU setup, but realized these are rare/expensive on light laptops. I am debating:

1. Would a lightweight laptop with a built-in dGPU be cheaper than focusing on eGPU compatability?
2. Buy a cheap ultrabook and build a Desktop PC?
3. Is there a specific laptop that fits all these criteria? Specific Models Considered: Framework Laptop 16 (Too heavy?), Framework Laptop 13 (Ideal weight, but no eGPU port planned).