Does intel actually have success in this space outside of forcing government entities to use their foundries for what I assume is national security level projects?

Quick google on who their foundry customers are appears to be mostly defense sector.

I have heard that intel has not been the best at working with other customers because they have been so vertically integrated for the entirety of their business it was difficult for them to work with others.

Why would one assume this one will ship on time when the other projects from the company are either years late or cancelled?

Intel foundry announced sometime around March 2021. https://www.theverge.com/2021/3/23/22347250/intel-new-factor.... Anything actually come of that yet?

edit: found a claim for $300M in revenue from defence firms, https://www.investopedia.com/intel-shares-pop-after-foundry-.... Can totally see US chips for US defence keeping Intel sort-of alive indefinitely.

Intel has stated that their foundry services will act independent of their chip designing division i.e. intel chips will have to compete with 3rd party chips for intel foundry time.

So yes, Intel (Intel foundry services) intends to be a direct competitor to TSMC.