Chase will deny you for most of their cards (including Southwest cards) if they find 5 (or more) credit card accounts on your credit report with an "open on" date in the past 24 months. Chase has also put restrictions on how many Southwest cards you can open, to make it harder to get CPs purely from credit cards, now that Southwest is starting to fly to Hawaii.

Most banks don't report business cards to EQ/EX/TU, and thus Chase's 5/24 count doesn't see those. (But Cap One and Discover do report their business cards to credit bureaus, and so their business cards do count toward 5/24.)

Citi will deny you the bonus (not the card) if you opened or closed that card (or another card in the same "family") in the past 24 months.

Amex has a "once in a lifetime" rule for bonuses, and on top that has recently started denying the signup bonus with a popup to people who've opened Amex cards, used them only for the minimum spend for the signup bonus, then "sock drawered" them and closed them when the annual fee came up after 12/13 months. (We don't know how how many years they look back for this, but it seems to be at least 2+ years.)

Compared to the above, the timing between one card and another card, if you're only going to apply for 2 cards this year, isn't critical. Just make sure you can do minimum spend on both without buying gift cards (Amex in particular will deny you the bonus if they "smell" you buying gift cards).