How do i check competitors email marketing without a big budget?

sign up to their list. that's genuinely most of it. use a separate inbox just for this so it doesn't get buried, and keep a sheet: date, subject line, what the offer was, how often they send. after a month you'll know their cadence and their welcome sequence better than most paid tools would tell you. if they're ecommerce, add something to the cart and leave, you'll see their abandoned cart flow too.