I used a Savage PTA based 7-08 in short / mid-range FR-Class for several years. I still have it, but the competition has got too 'hot' for it now in mid-range at any rate with 284 Win ballistics virtually the minimum necessary on a tricky, windy range.
It's capable of exceptional precision with a load combination it likes. A lot will depend on how the chamber in the rifle you have in mind is throated. The standard SAAMI 2.800"-COAL designed for short-action repeating rifles is very limiting because of the constraints placed on the use of heavier, hence longer, bullets - ie those over 140/145gn. (However, recent factory rifles in whatever chambering tend to come shall we say 'generously throated' no matter what SAAMI specifies.) My rifle is chambered for the 168gn Berger VLD and Sierra 160 TMK/ Hornady 162 ELD-M right on the 3-inch COAL mark. There are some lighter / shorter 7mm match bullets around such as the 130gn SMK if COAL is a constraint. My favourite 200/300 yard load was a mild one using the superb, if lowish BC, 150gn Lapua Scenar-L over Lovex S065 (Shooters World 'Long Rifle' in the US) loaded in elderly and very well made Winchester brass given some batching and preparation. As always, bullet to barrel compatibility is variable and crucial of course.
To use any of the excellent heavier 7mm bullets from the 175gn Sierra MK upwards, you need yet more freebore than my rifle has, twist rates may become an issue too.
You can see what the rifle / cartridge can do here:
http://www.targetshooter.co.uk/?p=3624
part of a series of H4350 alternative powder tests I did in 2020. The barrel count was rather over 2,000 by this point, so precision was a little below its original best.