Many many dollars can make many things happen. But since there is insufficient head room without excavating that out a long way, making that habitable will take many more dollars than most projects. That money would be better spent on a home that has the habitable existing square footage that you need.

How much would it cost? I need at least 9 feet height with electrical and HVAC connections. Even though we have to excavate, it is loose dirt. The whole place was fully excavated while building foundation. After building the pillars the place was filled with dirt later.

Costs are locale specific. Expect Several hundred thousand in an urban area, and be pleasantly surprised if it is less. You will end up reduced space in the basement for the cheaper route, as you can’t disturb the foundation. Or you lift it up, disconnect all the services, and remove it from the foundation, and then create a new foundation. The whole thing is risky and expensive.

I hope not to lift up the whole house and have a new foundation. Just want to replace the 3 pillars with beam and excavate the room down to 9 feet. Hopefully that does not cost 100s of thousands.

Your current foundation is a crawl space with a couple of columns supported on concrete footings. You can't simply excavate down; there would be nothing to support the footings. To convert the space to a basement, you'll need to do as PM described above. An addition to your home would provide higher quality living space at lower cost.