Regarding tuning devices, I use a Korg GA20 which must accompany me for over 20 years now. Can't remember of having ever changed the battery, lol. Has a jack input and mic. It is standardised to 440 Hz. and you can't adjust that but at least it tells you the marginal deviation as well. If I'm bored I'll look into this when I hit A4 and it shows I'm off -5 Hertz, that if I tune the other strings with the same position of the indicator to the left, that it's not becoming too dissonant. It is meant for guitars because it won't show notes that are not on the standard tuning of EADGBE (like with my baritone ukulele which has: GCEA, tuning it requires playing around with its offset button that allows an offset of 1 - 4 semitones down). Interestingly enough, it is not having any problems with octaves, but it just can't tell you that you're hitting F or C or any of the "black keys" directly. You just have to think a little (or work with natural harmonics after tuning one string, which is way funnier anyway).
I do have a smartphone app, called soundcorset, does the job just right, when I'm without the tuner. This also has a metronome functionality that uses the the smartphone torch. I used this only once and when you're rehearsing in a group without drummer, this worked quite well.
Funny enough that not even Ableton Live (Bundled with the Focusrite Scarlett audio interfaces) appears to have a tuning plug-in out of the box. But I'm sure I'd find one within minutes.