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Then, please, could you help me understand whether a device with the specs found below does (or does not) satisfy you:

HP EliteBook x360 1030 G2

• Processor: Intel Core i5-7200U
• Memory (RAM): 8 GB DDR3 RAM
• Storage: 256 GB SSD
• Display: 13.3-inch touchscreen, 1920×1080 pixels
• Network connections: Wi‑Fi with 5 GHz support
• Display outputs: HDMI
• Connections: 2× USB 3.0, Bluetooth
• Extra options: Bluetooth, card reader, HDMI, touchscreen, USB‑C, backlit keyboard, webcam
• Graphics card Intel HD Graphics
• Operating system: Windows 10 Pro
• Keyboard layout: QWERTY
• Weight: 1.28 kg
• Dimensions (L × W × H): 218.5 × 316.9 × 14.9 mm
• Price: €235,-

If you don't want refurbished, then how about the following device?

HP Chromebook x360

• Processor: Intel Processor N100 (Alder Lake, quad-core, up to 3.4 GHz turbo)
• Memory (RAM): 4 GB DDR5
• Storage: 128 GB eMMC
• Display: 14-inch touchscreen IPS, 1920×1080 pixels (Full HD), 60 Hz, glossy
• Graphics card: Intel UHD Graphics (shared)
• Operating system: Google Chrome OS
• Network connections: Wi-Fi 6 (802.11ax), Bluetooth 5.3
• Connections: 1× USB-A 3.0, 2× USB-C 3.0 (with DisplayPort Alt Mode and power delivery)
• Extra options: Touchscreen, 2-in-1 convertible, backlit keyboard (not present), HD webcam (720p), card reader
• Keyboard layout: QWERTY
• Weight: 1.37 kg
• Dimensions (L × W × H): 323 × 210.3 × 20.4 mm
• Price: €419,-

And, finally, if you actually want somewhat modern hardware, how about this one?

Lenovo Chromebook Plus 2-in-1 14

• Processor: Intel Core 3 N355 (1.9 GHz to 3.9 GHz turbo)
• Memory (RAM): 8 GB LPDDR5-4800 (soldered)
• Storage: 256 GB UFS 2.2
• Display: 14-inch WUXGA (1920×1200) IPS touchscreen, anti-glare, 300 nits, 60 Hz
• Graphics card: Integrated Intel Graphics
• Operating system: Chrome OS
• Network connections: Wi-Fi 6E, Bluetooth 5.3
• Connections: 2× USB-A, 2× USB-C (with Power Delivery & DisplayPort), HDMI, Combo Audio Jack
• Extra options: 2-in-1 convertible, touchscreen, backlit keyboard, Lenovo USI Pen (Gen 2) support, haptic touchpad
• Keyboard layout: QWERTY
• Weight: 1.40 kg
• Dimensions (L × W × H): 320 × 223.5 × 19.9 mm
• Price: €549,-

As many others have already pointed out: it's currently not the best time to buy hardware. FWIW, you could have grabbed Star Labs' StarLite^[Which, quite literally, happens to be a "tablet with a keyboard".] last year for 750 €. Currently, it starts at 1014 €.

Btw, OP, perhaps I'm obnoxious/oblivious/obtuse (or what have you), but I wasn't able to parse what you mean exactly with Linux compatible hardware. If it's not too much trouble for you, could you be very explicit?

EDIT: At one time, the StarLite was available for 416 (!) £. At least, as per this article of GamingOnLinux.