The simplest (but not necessarily most effective) way to improve the performance quality is to either export MusicXML or MIDI from MuseScore and open it up in a different software package that can either automatically add humanization or performance data or a package that makes it easy to add and adjust humanization.
As Laurence noted, if you export to MusicXML and then import to Finale, Sibelius, or Dorico, each of those three will create a much more human performance from the same MusicXML data compared to MuseScore. MuseScore has very little in the way of performance humanization.
Alternatively, and more powerfully, you could export MIDI and import the MIDI into a full-featured DAW such as Cubase, Logic, or Pro Tools. All three of those packages include mass MIDI editing tools that you can use for adding randomness to both timing and velocity. Other DAWs may have similar tools and capabilities, but I'm not sure. Randomization is only going to get you a small benefit. It won't sound as good as the humanization of one of the above programs.
The second-best-sounding approach is to use a DAW and make a long series of tweaks to the MIDI data, using what you know about the actual instruments, and also taking advantage of the tools in better sample libraries. For example, a lot of string sample libraries will have different samples for different techniques, like pizzicato, tremolo, etc. So you would go through and make sure you program in the sample switching for each technique. For regular techniques, you also want to make sure there are performance tweaks, such as selecting every other note of eighth note or sixteenth note runs and sliding the timing slightly and bumping the velocity to imitate left hand/right hand switching or upstroke/downstroke or whatever is appropriate for the instrument. I know you don't want to spend all the time to do this, but without this level of effort the results will also be mediocre at best.
The best sounding approach is to hire musicians to perform it for real. Some instruments, such as percussion, can sound very good with sound samples and slightly humanized playback, so you could hire only a couple musicians for the more sensitive instruments. If you have a whole string section, you could just hire one violinist (say) and have them record several takes and use that and some delay and chorus effects to create a much larger sound.
