Can hydraulic disk brakes be incrementally upgraded?
The M395 are a pretty basic but totally adequate brake set. Their benefits (very little setup and maintenance) are also their short-coming: you really can't adjust much in terms of engagement or lever free-pull. You're not going to be able to change much to adjust the feel.

It's also important to recognize that different manufacturers' brakes have different characteristics. Shimanos are known for their binary engagement - they have great stopping power but many people feel they are either on or off. SRAM generally get praise for modulating braking power but maybe not as much pure stopping power. I don't have much experience with Magura but they are know for their setup and adjustment options. Within a single brand the models are also going to differ (a 4-piston brake has lots of stopping power regardless of manufacturer).

I wouldn't recommend trying to upgrade an entry-level brake set piece-meal. As far as options for replacements - first: are you happy with the braking performance? can you live with or adjust to the amount of lever pull or engagement? If maybe, give this set a bit of time and you may be fine as is.

I like Shimano because they use mineral oil vs. SRAM that use DOT 4/5.1 oil (it can be a little nasty to paint and other surfaces) - it's a whole different argument over which is "superior". If you stick with Shimano you can re-use your rotors; if you switch brands you may have to replace them as well.

At about x2 the price of your 395's ($35) is the SHIMANO SLX ($70). It is excellent quality for the money that has a shorter "pull" and tool-free contact adjustment (like your Maguras). I almost always step up to the SHIMANO XT ($90) which is only a few bucks more. The entire M-8000 line (brakes, drivetrain, etc) hits a real sweet-spot for me in terms of price vs. performance. If you go SRAM I'd suggest looking around the GUIDE price-point which is going to be much closer to $100. These are all per-brake prices.

Whatever you decide, replacing brakes is a job you can do yourself with only a hex or torx key (depending on brand). Brakes all come pre-bled and usually are good to go (sometime you need a bleed to remove the spongy feel). There are two exceptions: if you need/want to run the brake lines internally you'll need to remove the hose and then bleed the brake and sometimes the hose is ridiculously long and needs to be trimmed (and the brake bled). Neither is super hard but you require specific tools that the average mechanic doesn't own.

Brake upgrades are one of the best value for money things you can do for your bike. I'd also suggest wider bars and an adjustable seat post. All three upgrade the enjoyment and level of your riding!