Buying a home in cash vs keeping dry powder

My wife and I are buying a house for ~$2M in a VHCOL city. If we were to buy it in cash, this would use up substantially all of our liquid investments. We were quoted a 6.4% APR on a mortgage. How much down payment would you do here?

HHI: $300k in base salary.

Expenses: without considering housing, $5k/month.

Assets:

• $2M in liquid investments in taxable brokerages. The good thing is that the tax has already been paid on these, so liquidating wouldn't result in a large tax bill.
• About $200k in retirement accounts, which I guess could be relied on in an absolute emergency.
• $3M in rental properties, about $1.5M in equity and $1.5M mortgage. These pay for themselves and are a pain in the ass to sell so I generally just ignore this.
• Low 8 figures in early-stage startup equity. Probably going to consider these worthless for this decision making.

My gut says to keep $100k in dry power for emergencies and put the rest into the house, thereby locking in a 6.4% guaranteed return by saving on the mortgage costs. I am not confident stocks would outperform in this uncertain economy. The only potential downside is if there is a golden investment opportunity to deploy cash, for example, after an '08 style crash, but banks won't give me a HELOC bc the housing value has fallen or they are just not lending. Another drawback is that my portfolio allocation would be 90%+ real estate.

There is ofc a spectrum here from 20% down payment to 100%. What would you guys do?