One thing you could do as trustee (using your example of $41k in dividends and a $3k capital loss) is not to distribute $41k (if the trust instrument gives you that discretion) in that tax year. Instead distribute $38k or something less. Say $38k. That gives the trust (assuming no other deductions) $3k of dividend income and the bene $38k of dividend income. At the trust level the $3k loss would wipe out the tax.
The next year, if the trust instrument/state law allow you to distribute more than taxable income (e.g. principal or even maybe even trust accounting income (if defined usefully) or the ability to make an allocation from principal to income), you could distribute the $3k from the prior year along with any dividends. The $3k would be (for 1041/tax purposes) considered principal and would not be taxed.
In fact if you have enough discretion as trustee look at filling to fill the lowest trust bracket with income. Especially to the extent the income is long-term capital gain or qualified dividends. For 2021 up to $2650 of LTCG/qual div for trusts is taxed at 0%! If that is less than the bene's rate (0% up to $40k single/$80 married) it can be worth doing. admittedly it is a small optimization.
[Note that LTCG/Qual divs to be taxed @ 0% are the last income that counts in that bracket. So for a trust in 2021 if you had $1k of ordinary divs and $2650 of qual divs, only $1650 of the qual divs would be taxed @ 0%. The rest would be taxed @ 15%. Take a look at 1041 Schedule D part V (lines 30 and 37 and what goes into them).
Also not that most trusts and state law allocate capital gains to stay with the trust. But not all do. A trust can allocate capital gains to a bene. You just have to have the authority and be consistent. Particularly in the modern age of total-return investing with low dividends and high capital gains, it is very reasonable (perhaps necessary) to think that way.
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