Of the $538.00 in market value for all other assets, what annual operating income can be attributed to this portion of assets?

First, bear in mind that it's $538 in gross assets, not net assets.

But I come up with $17.20 to $18.40.
The lower number is the last four quarters. The higher number is a "cyclically adjusted" number taking out the bulk of the BHE wildfire losses.

But I didn't kill myself ensuring accuracy, so take that number with a grain of salt.
Here's what I did:
Normally I value a share based on investment assets per share (adjusted downwards for the perpetual drag of having to hold a lot of low-return cash), plus a multiple of the after-tax earning on everything that is NOT an investment. The "everything else" I use is rails, utilities, manufacturing/service/retailing, and a cyclically adjusted estimate of underwriting profit. I took that "earning on everything else" number and scaled it to a $1000 investment at today's price.

It's off by a bit because in this thread the division is equities/cash/other, not (equities+fixed income+cash) versus (other).
i.e., the "other assets" figure of $538 implicitly includes the fixed income holdings. There isn't a whole lot of that these days, so it's not a huge difference.

Perhaps a better way to look at it, to keep things consistent within any given model:
I estimate that investments per share 396379 at end Q2, or $592 for each $1000 invested.
Everything else from your $1000 investment, including both operating units and liabilities and market-value multiple/discount, added up to $408 of your money invested.
Those $408 had, after interest etc, after tax income of around $17.20 to $18.40.
So, imagine Berkshire did a spin-off of all investments per share. You would get a portfolio of $592, plus a rump share containing everything else which would then be trading at $408, which had a variety of assets and liabilities.

It's late and past cocktail hour, so don't take this as gospel : )

Jim