Sorry it took me so long to get back to this, I kept forgetting about it and finding it again when I wasn't in a good position to write a good response, but kept meaning to. I think to address something pretty central here, the term "border crisis" isn't any specific event or events, it's the general term the media uses to hold up refugees and illegal residents as a spectacle to fuel reactionary politics. But it's really not just about the state of Texas being pricks about it, it's the whole situation.

Do the small bourgeoisie like immigration in the US?

Broadly speaking, suburban and rural petty bourgeoisie tend to be the most vociferous Republicans and compromise its primary funding network, and are the iconic exploiters of illegal migrants - things like restauranteurs hiring them as dishwashers and bar-backs, or landscaping companies hiring them to do yardwork. Urban petty bourg are more split between the two parties, for a number of reasons, often stuff like the politicization of race in the US.

outrage (I saw reported - maybe its untrue) come from when border states started moving migrants to cities?

The federal government has spent billions of dollars creating resources to house these people at the border when they cross. Texas shipping them around sends them to places that have no idea what to do with them. IIRC New York City had to set up ersatz shelters in public school gymnasiums so they didn't have to sleep in the cold.

is the 'crisis' simply a matter of those states wanting in on the public money tree that the Biden admin and backers have been enjoying with Ukraine?

No, because if it was, Democrats would happily throw it at them. The reaction from state governments and federal Republicans is just political showmanship, because they refuse to give Biden a win, especially during election season.

do you know or suspect if the 'crisis' relates in any way to the spats with Mexico

Definitely doesn't, nobody really cares about Mexico right now. If the US had any serious spats with Mexico, AMLO would be out of power before you could say "banana republic."

any way to the infamous intelligence agency directed drug trafficking business across the border?

They come here because a lot of their countries are in shambles with poverty and crime and political instability, which stems from US intervention in a big way (yellow-Parenti-dot-jpg). When the three letter agencies were smuggling coke in, they had their own airplanes to do it with, registered under a separately-owned company. Drugs do get smuggled in across the border, it definitely happens, but I don't think they're typically strapped to starving migrants. Makes more sense to hide it in crates or strap it to the bottom of cars.

Are they mostly from South/Central America

Most border migrants are, but most people who are illegal residents in the US are visa overstays from countries that participate in the Visa Waiver program. Nobody gives a hoot about those at all, so there are some seriously racist undertones to the border "crisis."

Are the people coming from the South useful at all to the Dem's usual backers?

Indirectly, in that they push the price of cheap labor down, which has a number of effects downhill that help them (more people train for the skilled labor that Dem backers tend to employ, goods are cheaper, etc). And it does see some benefit for Dems as a party - because of the politicization of race in the US, Latinos are broadly a fairly reliable Democratic voting block, with some exceptions like the Cubans in Florida. But you can't vote if you don't go through the grueling process of obtaining a citizenship, so while there's no direct effects there, we are now seeing the later generations swell the ranks.