None of what you're seeing is unusual for a machine of that age.
The centerpost is considered integral to the baseplate. There have never been factory-provided replacements of just the centerpost. The entire baseplate would have to be replaced and they're long not-available unless a servicer somewhere happens to have an old-stock item.
Combo52/John Lefever has described sourcing a stainless steel sleeve of proper size to fit over the centerpost and welded in place to deal with rusting.
Someone else "arris" removed his baseplate, took it to a metal fabrication shop for them to source and install a new stainless steel centerpost into it. Probably cost $$$.
Both are discussed in these threads from 5+ years ago:
61 Kenmore Washer
70's Lady Kenmore Agitator Removal
There are probably other threads where the procedure is mentioned.