I really like Mauser 98 type actions. But there were several million made as military rifles. They were tough and strong, but towards the end of wartime production a little were made of poor materials with conscript / slave labour. If using an old action to build a rifle you need to be sure of its provenance.
These days most of the poor actions are long gone. History has preserved the best. And modern clones - Prechtl, Mayfair etc are made at a level of quality well above a military original.
Difference between a military and a beautiful sporting rifle is many hours of time spent by a skilled craftsman perfecting the fit of the parts.
I also really like the old Mannlicher Schoeneur’s, indeed I would prefer a full length barrelled one in 6.5x54 over and above a Mauser. I don’t like the short full stocked ones.
These rifles were originally built in the days when open sights were the norm, telescopic sights were expensive and fragile. And the object of stalking was just that - stalking. Get in close and take your time to shoot properly. They were stocked and balanced to be shot using both hands to properly hold the rifle, and you need a firm hold to shoot them properly.
They are not heavy barreled chassis rifles with free floating barrels needing bipods and shooting tripods to take even a close range shot.
They were designed to be carried lots and shot little, but when the shot came to deliver acceptable accuracy.
In colonial times, the light rifle also did double duty when sorting out local difficulties. They were fitted with sights graduated out to long distances. These were not so much for trying to put an impala into the pot, but to provide harrying fire on bandits, locals who were anti colonial or dastardly members of an opposing colonial power. So farmers, hunters etc bought Mausers, Mannlichers and Enfields to both shoot game and protection.
Remember that in the early days of smokeless small bores, military officers also had to provide their own weapons, hence many of the above rifles.
Personally, being left handed, they all have a major draw back, but you can learn to live with it. But not the same as a proper handed rifle.
Push feeds work well and do the job. Many such actions do however use a spring powered plunger in the bolt face. These do need compressing and thus positive forward pressure on the bolt handle. But you get used to that.
Will these old rifles shoot. Depends. I have had a shot with an original open sighted mauser. With hand supported on a pack across a pickup bonnet keeping every shot inside a clay pigeon at 100 odd yards is straight forward enough. And in good light, with a good visible target you do better. Will you shoot half MoA all day long - probably not. Minute of deer vitals to reasonable distance - not a problem with practice.