Seattle > Los Angeles > Brisbane (Australia): Do I stay airside at LAX?

If I am doing SEA LAX (DELTA), LAX BNE (VA), can I stay airside at LAX and avoid LAX TSA.etc?

Long story short:

• First time travelling to the USA. Heard plenty TSA / CBP / LAX horror stories. Want to make sure I've got all my ducks in a row.
• Short layover (< 2 hours) in LAX.
• AU citizen travelling on AU passport. Visa waiver program.
• Booked as a single trip.
• Delta SEA LAX and Virgin Australia LAX BNE.
• Virgin and Delta are partners - the Delta flight is codeshared to Virgin Australia, and the whole trip was booked via Virgin Australia.
• I am checking baggage which I want to go all the way through.

I have read the following:

• https://www.virginaustralia.com/au/en/experience/at-the-airport/airport-guides/international/los-angeles/
• https://www.virginaustralia.com/cs/groups/internetcontent/@wc/documents/webcontent/~edisp/lax-connecting-flights-2019.pdf

My itinerary states:

• The Delta SEA LAX flight arrives at T2
• The Virgin LAX BNE flight departs from T3. I believe this to be false as surely VA would fly out of TBIT as this is where their flights arrive? I believe VA checks in at T3 but flies out at TBIT. This seems to be what the above documentation says.

I have concluded:

• I will arrive at LAX T3
• I do not / cannot claim my baggage as it will be tagged through to Australia without me needing to transfer it.
• Thus I can stay airside at LAX and walk or use the free shuttle to get from T3 to TBIT.
• I board at TBIT avoiding LAX security.

I was concerned about outgoing immigration/passport control in the US but I've been led to believe that this is all electronic in the US and occurs when you check in with your airline.

Any additional insight is appreciated. Thanks.