If you’ve seen any Shakespeare plays you can enjoy it & the more you know the funnier it is - I should know since my mum loved Shakespeare & I’d been dragged to see “Hamlet” 8 times by the age of 14! But David Mitchell (Shakespeare) is basically himself in a 16th-century setting so there’s lots of references to contemporary problems like public transport, which he frequently rants about as a commuter between London & Stratford-on-Avon, corruption, government incompetence etc. There’s also the ongoing gag of him being amazed or offended whenever the rest of the cast criticise his work for what everyone who's ever studied his plays at school knows is typical Shakespeare: long-winded obscure dialogue, unfunny comedy scenes, unconvincing cross-dressing, etc. Worth watching if you’ve never seen it.
As for the Agatha Christie serial I’m no expert, but it’s not like most past dramatisations, in fact she’d hardly recognise such a dark, sluggish adaptation of her work.
That stuff is only 'typical Shakespeare' if you don't like Shakespeare. However I don't wish to have an argument. The show works well as a lightweight comedy.