How to bring both of the video footage to the same level of colour / lightning

The second, brighter shot looks like an HLG clip, maybe phone camera? ... not properly color managed onto a Rec.709 timeline.

Make sure you have your color management setup correct. Lumetri panel, SETTINGS Tab. The one named Settings. That's where all the CM controls live, and there are a lot of them!

Display color management, auto detect log, and auto tonemapping should be 'on' for most workers in most workflows. As a start.

Set your working sequece color space to Rec.709, and use only export presets that do not have HLG or PQ in the preset name. Those are HDR export presets, which do not work with SDR/Rec.709 exports.

Try Lumetri > Match Color (color wheel & match)