We have to intuit it. Does anyone say they are a “third way” politician? I’m not sure even Clinton did and it is mostly tied to him.
No, we don’t.
Stick your head in the sand if you want. Ignore the dangerous thing. Maybe if you can’t see it then it can’t see you. Good luck.
There’s a persuasive argument if I ever saw one. 
You haven’t brought anything besides your own say-so to connect Pelosi with Clinton or this “Third Way”. The Wikipedia article on “Third Way,” if you do a control+F search for Pelosi, has no mention of Pelosi. The WP article on “Political positions of Nancy Pelosi,” if you do a control+F search, contains no such string “third way.”
California has a top two primary system. The candidates who come in first and second in the primary run against each other in the general election. It is fairly common for that to be two democrats.
As speaker, she played a good ‘Mom’ to el donald’s ‘toddler throwing temper tantrum’.
The function of US House Speakers, Conference Leaders and Whips is to keep the legislative body functioning and get the important legislation passed, or if in opposition get a compromise; and to help their caucus members get and keep seats. And she was good at that. You could ask the average American what was the great accomplishment of each of the last 100 years’ worth of Speakers and they could not tell you off the top of their heads either.
And seriously, not going to reproach her not meeting in the 1990s the 2025 popular expectation of a Progressive. That said, yeah, 40 years is a bit long to stick around. You DO wind up falling behind in some things and accumulating histories that can be used against you.