Which is better for a bright living room?

Neither is the brightest option; OLED excels in controlled light. Between the two, the G6's newer α11 Gen3 processing handles tone mapping and reflections better, so it is the stronger pick in a room with some daylight.

Is the G6 worth stepping up to over the G5?

Yes for most buyers. The G6 adds the Gen3 processor, a 4.2-channel 60W speaker system, Bluetooth 5.3 and QMS/QFT on its HDMI ports. The G5 makes sense only if you already own one or want the prior evo generation.

Both use the same self-emissive OLED panel type with similar lifespan expectations. The G6's newer processing and connectivity are likely to stay current longer as streaming formats and consoles evolve.

Do both come with a wall mount?

Yes. The G5 ships with LG's gallery-style wall mount, and the G6 includes a wall mount kit with a 600 x 400 VESA pattern. Both are designed to sit flush against the wall.

Can either handle PS5 and Xbox Series X at 4K 120Hz?

Yes. Both have four HDMI 2.1 ports with 4K 120Hz, VRR and ALLM. The G6 adds QMS and QFT, which reduce black screens when switching between sources and frame rates.

Do I need a soundbar with either?

The G6's 4.2-channel 60W system is decent for everyday viewing, but at 97 inches a dedicated soundbar or AV receiver still improves the experience. The G5's built-in audio is weaker, so a soundbar matters more there.

LG OLED evo G5 97-Inch vs LG OLED97G6WUA OLED TV

Both are 97-inch LG OLED evo wall-mount TVs, and the G6 is the newer generation with the α11 Gen3 processor, four full HDMI 2.1 ports and a 4.2-channel 60W speaker system. The G5 is the prior evo G-series set with the same 97-inch self-emissive panel and gallery-style wall mount. Buy the G6 unless you find the G5 at a clear value advantage; the G6's brighter processing and newer connectivity are the safer long-term pick for a dedicated home theater.

Choose the LG 97-inch OLED evo G5 if you want the proven evo G-series panel and wall-mount design and the G6's extra processing and audio are not worth the step up to you.
Choose the LG OLED97G6WUA if you want the newest 97-inch LG OLED with the α11 Gen3 processor, four HDMI 2.1 ports and a stronger built-in speaker system.

Prices

LG OLED evo G5 97-Inch: $16,249.99 at Amazon (last seen Nov 10)