The power system on my solar shed is, admittedly, somewhat overkill in an attempt to get through the winter without having to light the generator (so far, I've failed at this, our inversions are nasty). The flip side is that I have quite a bit of surplus power most of the year (on the order of 10-15kWh/day). If I use it, great, if not... it just doesn't get pulled out of the panels. The office is standalone (and way more trouble than it's worth to grid tie), so when the battery bank is full, there's nowhere to stick extra energy.
I've considered various methods to use some of the surplus in useful ways, which so far has looked like donating a lot of compute to various BOINC projects (including cpdn, which is now out of work...). But I've not seen much work in the way of "things that could actually capture concrete amounts of carbon and store them" at this scale. It's all huge facilities, big multinational investment, etc.
I've considered an algae grow system that would cycle air through some grow tanks (I have a lot of sun, growing algae in containers is sort of the default around here) and then bury the algae down some holes, but I'm not sure it really accomplishes that much.
Another option I've considered is making use of some of the basalt laying around, getting a rock crusher to grind it into powder, and then either spreading it on the hill, or trying to find some sort of more rapid system for weathering it (tanks of water with airflow through them?). Of course, if algae likes basalt... I could combine the two!
I just can't find any information on smaller scale systems like this, and I lack the bio and chem background to really be able to do things like analyze rock dust for carbon content.