Air carrier Captain reported extreme fatigue due to the companies scheduling and personal activities. The Captain called in fatigued to the company and was removed from flying duties.

Narrative

I'm involuntarily TDY'd to ZZZ; and had been on duty for 2 days at the time of the event. I have been commuting to ZZZ for [8 hour] airport standby (ready Reserve) for 17 days in the last 30 days; and I have been to my home for 2 days the entire month due to TDY. The night of the Date I was unable to get sufficient sleep; because my significant other (herein refereed to as SO). has been looking at houses with me over facetime and we have conflicting schedules. On the [following day] I was on airport standby with no calls for 8 hours. I was assigned a flight to ZZZ1 that was scheduled to depart 30 minutes after my shift ended. The flight landed and we got to the hotel by XA:00. I then had to find suitable dining accommodations. I was able to get to sleep by XS:00 for a XA:20 van after looking at homes with my SO whom I have barely seen for the last month. During flight; I began to notice error compiling due to fatigue. I immediately alerted the First Officer to my increasing levels of fatigue and asked him to keep a high level of vigilance as I began to feel I was making mistakes; and missing radio calls. As we were descending through 12;000 ft. back into ZZZ I realized we had also forgot to set local altimeter setting. We landed with no further incident. However as we arrived at the gate I have been assigned an additional 6 hours of flying to ZZZ2 and back. It was at this point I decided to remove myself from flying duties. We often hear about the 'swiss cheese model' In aviation; where it is not just one issue that causes incidents in flight; however it is often multiple issues that overlap and fatigue is almost ALWAYS a major contributing factor. In this case; I was beginning to see the holes in our hypothetical model line up. Flying around 79 other people; there are no excuses for poor performance. I do not want fatigue hindering from performing not only my duty to the passengers and company; but preventing me from safely operating the aircraft is unacceptable.The root cause is accumulated fatigue due to poor staffing; forcing me to two-leg commute to an unintended; and unwanted base whilst also being asked to live out of a hotel room for 30 days. On standby I've had a constantly changing schedule that could be remedied with better staffing. After working a full day of standby being asked to work a flight thats 30 minutes after my shift ends for a short overnight; then having a flight day of 7.5 hours of flying is unrealistic.