I think you will find most fairways sets using the same shaft and then the heavier going to the hybrid clubs as they get significantly shorter in length.

Same shaft in the Driver and Fairways for me.

I try and keep same shaft and grams and flex for my Driver, 16.5 and Mini Driver for consistency. Seems to work fine for me. Switched to Diamana red shafts..

I used to play a 10g heavier shaft vs driver in my 3 wood, and 5 wood. Ie; 60g, 70g, 80g.

I recently switched to a 4 wood and a 7 wood, and found the same formula didnt work as well. Currently playing a ventus blue velocore plus TR 5s in driver, 60g ventus blue plus in the 4 wood, and a 70g ventus plus red in the 7w and really enjoy the setup. Previously never played a 3w shaft lighter than 70g.

I use same brand. 55 in driver, 65 in fairways and 75 in hybrids. All regular shafts.

I'm set up the same way --- 10g heavier in the fairways ...

This set up is based on my fitter's recommendations. He has never let me down. Each of my hybrids are set one degree strong. Great set up for me. I am a senior (79) and just do not have the swing speed I use to possess. My hybrids were 85gm when I was playing a 65gm stiff driver and hitting my drives over 250. My favorite hybrids were the 818s, 85gm with Fujikura Speeder Shafts. There were hot.

For me,
Drivers in 60 gr.
Fairways wood in the 70 gr.
Hybrid in the 80 gr.

But I am always verify that swing weights are in D3 .

It's an old assaumption that you need to step up the weight as you go through the line. Depends on what you are looking for from each club, and a club fitter can help you achieve your desired result better than the old assumptions. I play 3 different shafts for my driver, 3 wood, & 5 wood. All 60 gram class Graphite Design.
I tend to put too much spin on my driver so they gave me the AD-XC shaft. They assumed that due to my age I should be in a 50 gram shaft, but I was getting better results with the 60.
I use the 3 wood probably 80% off a tee and 20% from fairways and went with the AD-DI. A little more spin and higher loft, and the 60 worked best for me.
My 5 wood is pretty much a fairway & light rough club, and has the AD-VR shaft. About the same spin and loft as the DI but swings smoother, and again the 60 gram works best for me.
Stepped up to the AD DI Hybrid 70 gram for my U505 utility 4, and the 80 gram for my 5 hybrid. The U505 has been misbehaving for the last month, and I'm hoping it's just the seasonal flu.

I play the Ventus black TR 6s tipped 5/8 of an inch in my driver, and play a Obama Kiyoshi purple 7x in my 3 wood, I like that it gives me a little higher trajectory off turf.

I think when if I pick up a GTS 3 wood I’ll order it with a Ventus blue TR 7x

I play the Ventus black TR 6s tipped 5/8 of an inch in my driver, and play a Obama Kiyoshi purple 7x in my 3 wood, I like that it gives me a little higher trajectory off turf.

I think when if I pick up a GTS 3 wood I’ll order it with a Ventus blue TR 7x

Fitted at Titleist for driver (GT3) and fairways (GT1) and have the same weigh shafts in all clubs.
Just added a hybrid (not Titleist fitted) which has a 10g heavier shaft and I really feel the extra weight. It has taken a short while to get used to this.
I would absolutely recommend going back and having a specific fitting to make sure it fits with the rest of your bag and that you are comfortable with the new club(s).
All the best