Last time I checked which was a few months ago, but it should still work(?):
Host needs to send you an invite while in fortuna (you cannot accept this invite)
They start the PT bounty and load into orb vallis
Once the host is loaded into orb vallis on PT bounty, you now accept the invite.
If it still works, you should load into the PT bounty and be able to get rewards including the bounty reward. You have to do this for each hunt, but it's better than not doing PT.
Not like it's impossible to get to rank 5 solaris. Easiest way granted is to be helped by others to farm Profit Taker. But you need to get VS ranked up for eidolon hunting anyways, and you need eidolons to get arcanes like energize.
Can't you just buy them from little duck 1k a pop?
I quit playing duviri after week 5 of SP circuit, I couldn't take the constant return to 5 missions repeating ad nauseum. The amount of time required to reach rank 10 in SP circuit, and on top the 5 week rotation with 5 rewards per week.
Coupling that with DE has said they will be adding more incarnons has left with such a sour taste. It's far too repetitive, too grindy, and extremely time gated. I'd rather get two resources a week that I can turn into any incarnon, even if I can only ever hold 2 at once. And dear god we need more missions that can appear so it's not so repetitive.
I forget exactly how the solaris rep grind works, but I know you need debt bonds to rank up which the PT farm can vastly help. Also VS needs resources to donate for rep which PT gives. As for rep farming, iirc the best way to farm rep still to this day is conservation with Ivara/Equinox with archwing, since you can do free roam captures and quickly hit max rep in less than 30 minutes. Brozime should have a video on farming open world rep since he did a f2p playthrough recently