For mountain/trail running, you can move back and forth between using mileage and duration as the measure of volume. Because your pace on a technical, vert-heavy trail may be much lower than on a flat course, trying to achieve high mileage in such terrain will probably require more energy (and time) than you can expend in a week. On the other hand, races are still quantified by distance so being able to do the miles remains important.
Ultimately, you have to manage your energy and time during the week. If you want to do the long hikes you’ll have to accept that doing so will limit your ability to get your goal mileage for the week, but know that there will be some contribution to your overall fitness and strength.
As for how to log these efforts, the main priority is consistency so you can track over time what you’ve done and what worked best. If you anticipate mixing in these types of efforts on a regular basis and using them as part of your mountain running training, log them as running. Your mileage may be lower than what you initially planned, but you can observe how the total volume (by duration) of time on your feet contributes to your goal.
If you’re concerned about your ability to do a certain amount of miles over time, maybe consider alternating weeks or blocks of weeks, wherein some periods you focus more on building overall mileage through straight-forward running sessions, and other periods you allow a reduction in mileage in favor of bigger overall volume through hiking and scrambling/vertical gain.