05 suburban 5.3, keep getting "Reduced power mode"

[Blue85]

you have to use a scan tool afterward to tell the computer the battery has been changed.
Otherwise, it will keep using the older battery charging plan and damage your new battery......

Umm....unless you've cleared that setting by disconnecting the battery. I've never reset this and never had issues.

BTW, seeing all that brown crud in the first pic, makes me think you might benefit from a catch-can.

It's not an uncommon mod on these trucks. The PCV valve went went away for '04 or '05 and the function is achieved with a baffle in the DS valve cover. If the engine builds any sludge, the little drain-back holes in that baffle plug and the engine starts sucking some oil. The official fix is a new valve cover, but with some elbow grease and a good solvent (like EZ-Off!) You can clean an old one up. Some seem to use more oil than others, driving some owners to a catch can.

 

[Blue85]

The adaptive charging can be annoying. I have a power inverter that starts chirping above maybe 14V and below like 12. . And will trip during different charging conditions. When the engine is warm and battery full, the system voltage is maybe 13V and this isn't very good for jump starting a dead car. On some systems the voltage increases to charge your trailer battery, sometimes by sensing the load on the trailer plug and sometimes by the Tow/Haul button.