Am I missing an obvious product?
Start looking at solar charge controllers. Specifically higher-end models that have reliable current limiting capabilities. I can't guarantee that every product will behave this way nicely, but for the most part, connect the battery to be charged to the battery output connection, and then connect the "mothership" battery to the solar input. In that order, please, charge controllers don't like to be connected to the solar side first, could potentially fry them. The charge controller will treat the mothership battery voltage as a solar panel with available current, and draw from it accordingly.
I have done a similar setup, as I have a 14s Li-Ion home battery powerwall setup. I used the MPT-7210 boost solar charge controller to charge my 24s LFP motorcycle battery. I have also used a simpler aliexpress 1800w buck converter to do the same.
And here's where you'll run into your problem. Your source voltage and output voltage are far too similar. In fact, you specifically mention that your source battery is 16s LFP, and one of the batteries you plan to charge with it is also 16s LFP. So technically, if your home base battery was fully charged at 56ish volts, and your LFP ebike battery was depleted at 48v, then the charge controller connection method will work, for a bit. But at some point, your charging input voltage and your charging output voltage will be the same, and no current will flow. Hypothetically call it at 52-53v, which I presume is not charged enough for your ebike battery preferences.
I don't know enough about electronics, but it's possible that someone might know enough to custom design (or at least describe) a circut that can do what you want. You need voltage to be stepped down and current regulated from the big battery source, until the voltages are the same, then you need voltage to be stepped up and current regulated. Simply because your two voltages are so close, you're not going to find a single off the shelf component that will do what you want. In fact, even with the charge controller method I described in the first paragraph, you'll see decreasing current flow to 0 as the batteries get closer in voltage.
I have a messy and inefficient suggestion. 16s LFP mothership battery -> 48vdc to 120 or 240vac inverter, 2000w rated -> plug in battery charger of your choice. This will overcome the voltage similarity problem, at the cost of 2 conversion losses and excessive expensive equipment. Sorry.