This is a matter of matching up the exact plan you are in with Pub 36 and the other link. I did not read the second link to completion, but still would not have known exactly what plans you have participated in. The second link is very specific, while Pub 36 has always generated several questions. The term “pension” is very broad and it is not always clear what plans are considered pensions in addition to traditional DB plans. You might have been in several different plans given the number of different plans available and career changes you might have made.
Looks like 403b plans are not eligible for the full exclusion unless you happen to have been in the NYC Teachers Retirement 403b, which is an exception. Your 401a (also includes many types of plans) but if you did not contribute to it, it probably is eligible for the full exclusion.
Any plans not eligible for the full subtraction, but meet the restrictions of the 20,000 subtraction are subject to the 20,000 total subtraction for all such plans. A spouse receiving such payments would qualify for their own 20,000 subtraction.
Note that for plans not eligible for the full subtraction because you contributed to them should be only partially taxable when distributed, since you will not be double taxed on your already taxed contributions. As such there might be less to taxable income to subtract, making the 20,000 limit go further.