Code number P1133 Heated Oxygen Sensor Insufficent Bank 1 and Bank 2 2008 Suburban 5.3 Is this a problem that needs to be addressed at once or not. What could happen if I ignore the problem?

ALL things pertaining to ANY motor vehicle, needs immediate attention

There is too much theory & various possiblities to list here

I would not suggest you just throw parts at problem,but you have
DTC --diagnostic trouble codes that are active & are telling you that
an item in some system has failed,so yes, find out what & repair now

Your ability to use the vehicle at all or enjoy it with the confidence
that damage won't happen is not certain

That said I would replace the O2 Sensors in this case
You will have one or two that are in or before the converter
or converters, if you have two.

They should be changed at 80 to 100,000 anyway, and are clearly
not working correctly, based on the codes you provided

The rear sensors should be okey

I have no idea why you & thousands of people even suggest ignoring
something on any vehicle when problems arise
They cost $40,000 new & are treated like they mean nothing & have no
value or use in your life

I paid less than that for my first home.