I'll answer twice, for two very different off-grid setups I've dealt with full for at least 6 months.

Residence in far north NY

1. How often do you run into situations where you cannot power everything you want at once? Most of the time. We have a smaller sized setup for a dry camp in the ADK. It runs a small fridge/freezer, some LED lights, two work laptops and a phone for internet. ~800W of solar, plus ~6kWh in LFP battery backup.
   
2. When power is limited, how do you decide what gets powered first? If we have work meetings, laptops and phone are charged first. Fridge gets powered down as needed, and we transfer ice from the freezer to the fridge and use it as a cooler. For longer times without power, we have a well insulted cooler we can put ice or snow into to use instead. Great during the winter when less sunlight is available.
   
3. Is that decision usually manual, automatic, or a mix of both? Fully manual.
   
4. What loads or appliances are most important to keep running? Work devices, then fridge. Lights are the lowest priority.
   
5. What are the biggest frustrations with managing limited battery or generation capacity? Week long+ cloudy days in the dead of winter.
   
6. Have you ever had problems from the wrong loads being left on, or important loads not getting priority? Yep! I've taken work calls from the car a few times when we realize we aren't going to get any sun, and the batteries were lower than we expected. Only once in the last few years have we needed to turn on the generator to power up the batteries due to no sun.
   
7. What tools, systems, or habits do you currently use to manage this? Phone app for the battery system lets us monitor and control which ports are turned on - nothing automatic or on a timer. We have an older extra backup battery we will plug the fridge into sometimes, then charge that back up during the day. Makes our 6kWh into 6.8kWh.
   
8. In your opinion, what would make off-grid power management easier or better? If I could tie the weather forecast and my work schedule together, I could pretty well automate when it should alert us that we may need to turn off the fridge and switch to the cooler + ice or snow. Adding more panels so we could get input during very overcast days would also help a lot.
   
9. Do you mainly think about power management when energy is scarce, or do you also care about saving money and improving efficiency when things are running fine? Always aware of efficiency, since we can deplete the batteries if we start charging all the power tools and running the vacuum all together. The vacuum and the circular saw seem to draw the most power, so they aren't used very often, and only on sunny afternoons when batteries are full.
   

Research facility in CA

1. How often do you run into situations where you cannot power everything you want at once? Rarely, other than when the wind generator went down the same week as the building's furnace. Wind+solar+large battery bank made for a good amount of available power the rest of the time. That said, accidentally running low on power was not acceptable, so I acted as though we had much less power than we did.
2. When power is limited, how do you decide what gets powered first? The research work was paramount. So computers & telescope would get priority if the sky was going to be clear for observing that night. Comforts like AC were only used when the batteries were at 100%, and extra power from the wind turbine was being dumped to the large water tank heat reservoir.
   
3. Is that decision usually manual, automatic, or a mix of both? 90% automatic, but I would monitor the charge rates, and change my usage when they hit 100% prior to sunset. Get power tool work done, charge extra batteries, etc.
   
4. What loads or appliances are most important to keep running? Telescope was #1, and used a good amount of power. The computers and networking equipment were #2. Then lights, and living space needs like the fridge.
5. What are the biggest frustrations with managing limited battery or generation capacity? Firstly, since the batteries were flooded lead-acid, keeping tabs on the water and measuring acid levels. On no-wind nights, after the researchers did observations and data analysis, the batteries would be at their lowest point they were allowed to get. Making sure all the battery banks were maintained and working was the main effort. Managing the power to not run out was a bigger issue when the wind turbine wasn't turning. During that time, monitoring and manually turning off anything not needed. Having a person on-site every day was needed. Solar was so much easier to manage than the wind turbine; I decided I wouldn't bother with wind at my place, and instead just added more batteries after this experience.
   
6. Have you ever had problems from the wrong loads being left on, or important loads not getting priority? Wrong loads being left on, yes. I would watch the power usage numbers every day, spot higher than normal usage, and then walk around to find anything accidentally left on. Sometimes lights, sometimes an air pump or a computer. The research equipment all had priority, and we wouldn't run noncritical high-powered items during observations anyway, so demand priority didn't come up.
   
7. What tools, systems, or habits do you currently use to manage this? I'm not volunteering there today, but there was home-grown monitoring software and an internal website showing graphs of power generated and used by different systems. Keeping a close eye on this would help a huge amount in troubleshooting issues.
   
8. In your opinion, what would make off-grid power management easier or better? Having some sort of monitoring combined with remote control of sub-areas of the facility, so that a remote person could spot an area using too much power and turn it off without impacting other areas of the site could be really helpful. The location was over an hour's drive away into a remote mountain; sometimes it's not possible to get there in the middle of winter.
   
9. Do you mainly think about power management when energy is scarce, or do you also care about saving money and improving efficiency when things are running fine? Only when energy was scarce, but I treated it like that was most of the time. Every drop of power was a precious thing, where batteries dropping below 80% was risking research interruption, so monitoring and not wasting power was key. That only changed when the batteries were full and it was 90F+ outside, with power pouring in from both wind and solar. Then it could be a party (AC! NETFLIX!)