Go with subfolder (/blog), zero debate. Google treats subdomains like separate sites, meaning your main domain loses out on all the backlink equity, trust, and topical authority your blog builds. Only use a subdomain if technical limitations force your hand.
When you have an url domain setup like Seth Godin has, the blog on a separate tld domain link it well to your main business website who have pillar pages. That this setup not builds authority , that it will split your authorithy or is bad for seo, do you have found any hard facts in the web about this statement?
Yep, no!
Because it comes from SEO Agencies worldwide after MOZ made such a statement that multiple domains are bad for SEO- google itself not says this. Ok nowadays we see subdomains as example, not ranking good here is a subfolder the better choice, when you not want have multiple separate domains. Same with that old stubborn lie of DA a metric invented by MOZ, not by google, google not using this metric.
Seth Godin called them all "liars" and you see he is dominating google page 1-4 with his short blog posts.
My five cents is this: you want build authority, all on one website....
there you have a start page
work with me
what I do page
ressource page
about me
pillars important yes
then a blog with 3-4 categories.... etc,etc....
for me it looks like a mishmash not like a topical authorithy site.
Then have that blog separate on a blog domain you writing daily about your pillar topics link that blog well with your main business site - then the blog will have topical authorithy in my eyes.
Proof me wrong here.