Attorney should get 1099. IN GENERAL, the part for services provided to your client should be on NEC box 1. The settlement portion should be on the MISC, box 10.
The amount to include will depend on how the check was made out. My basic understanding is that if the check was paid to only one attorney, then obviously that attorney gets the 1099 for full amount. If one check is paid to co-payees, I think they each get a 1099 for the full amount. If attorney gets money and part is for co-counsel, then attorney gets 1099 with full amount, and they issue a 1099 for amount they paid co-counsel, but again, that depends on who check is made payable to.
There is also the issue on what type of settlement the payment is for. Example, as the article below explains, payments for personal injuries don't require 1099s to the injured party but will be issued to the attorney, depending on how the check is made out.
I'd suggest start your reading with the article below from the ABA that is written in more layman's language and is informative before going to the 1099 instructions for preparation, and then the code . The 1099 instructions do reference the applicable code sections.
Also, perhaps a separate post would be better for what portions of these payments are deductible by your client.
Slippery Pencil is correct that attorneys are an exception to the corporate rule. They get 1099s regardless.
Anyway, here is the ABA article to start with:
https://www.americanbar.org/groups/business_law/resources/business-law-today/2020-february/irs-form-1099-rules-for-settlements-and-legal-fees/