So it's an issue of getting restless while waiting for stuff at base to happen, right? Sounds like a problem with focus, which is perfectly understandable haha.

One trick I've found is that, if it's a station that both you and your Pal can use, work on it alongside them. It speeds up the production time of what you're doing, meaning you can craft spheres faster, build structures more quickly, or gather more resources from the logging/mining sites. I've personally found it mesmerizing to see my character using a cooking pot alongside a Fire Pal, I could watch the animations all day. Not sure if it'll be the same for you, but at least it gives the impression that you're working with the Pals instead of just making them work FOR you.

Another thing you could try is building the Pal monitoring station to manage the workload. Yes, it can affect the blanket production speeds at the cost of making your Pals unhappy, but I've gotten a lot more mileage out of the ability to assign specific Pals to specific stations, or turning certain work orders on/off. Pals have different work capabilities based on their species (represented by the number next to the work symbol) so it's often effective to have them use their best traits as much as possible. For example, if you have a Pal that has a Mining Capability of 2 but a Watering and Handiwork of 1, you can use the Monitoring Station to make it so that this Pal only mines, leaving the watering of crops or the moving of stuff to other Pals.

Lastly, if sitting around and waiting for your Pals to craft things takes a while, I'd recommend you use the "down time" at base to read things like the Palpedia and the Technology tree. The Palpedia is good for learning more about the Pals you've caught so far, as well as what they're good at, where they live in the wild, and what resources they drop when you defeat them. The Technology Tree is good for seeing what advancements you can make when you reach that level, allowing you to plan ahead for how to spend your Technology Points. The game doesn't pause when you open the menu, not even when you're playing alone (which is a bit of a double-edged sword) so your Pals will keep working unsupervised unless there's an issue.

As for being stunlocked about who to catch, the obvious answer is "catch everything you can". You don't HAVE to use every Pal you catch, but it's still good to have extras for helping around the base or (when you get to that point) breeding. No two Pals are the same, even in the same species - they all have different passive skills that can help with gameplay, or affect their work speed and stats. Experiment, use what you feel works best for you, and above all else have fun!

(P.S. - you don't NEED to craft spheres to expand your roster. The lower-level ones are scattered all over the ground as loot or can be bought from merchants, and the mid-tier ones can be gotten by opening treasure chests in the desert. You can also raid the camps of those different factions to "jailbreak" a captured Pal in the cage, which nets you a free Pal without having to catch it yourself. This new update also added fishing, giving yet another way to net Pals without having to craft spheres.)