Return to Paradise. London detective sent to small coastal Australian town where she grew up investigates and solves the weekly murder. Spinoff of Death in Paradise. Only six episodes.
Two of my favorite shows of all time:
Lodge 49, a surfer dude for whom life has lost meaning finds community in at the local Fraternal Order of the Lynx.
Mrs. Davis, most everyone on earth takes direction from an AI algorithm that tells them what to do. One nun and her ex-boyfriend are on a mission to destroy it.
Mrs Davis was at least a limited series but Lodge 49 was cancelled after only one season though there seemed to be larger mysteries to be explored in future seasons, so that was unfortunate.
I watched Lodge 49. I like Donal Logue. I remembered enjoying it. It definitely had a nice vibe!
Lodge 49 had two seasons and ended on a cliff hanger that actually was kind of a perfect ending if you were okay with ambiguity. It is my favorite thing Paul Giamatti has ever done.
In a lot of ways, Mrs. Davis is kind of the spiritual successor to Lodge 49, both about holding on to humanity in a dehumanizing society and both employ magical realism.
I just posted about the Netflix show ‘Sirens’ in ’ Series you’ve recently watched, are now watching or have given up on’, but since it’s a limited series with just 5 episodes, it fits here perfectly well too:
Does Julienne get sliced and diced? 
Haha, must have been thinking about what to make for dinner when I posted that.
Another one is Beyond Paradise - a Death in Paradise detective in a small Cornish seaside village and a very small and quirky team to work with. [I wonder what other programme’s audience they were aiming for :)]
I don’t think anyone’s mentioned Detectorists.
Outside OP’s timeframe, but gentle comedy dramas still worth re-running:
A police detective longs for early retirement to run a restaurant, but his devious boss finds ways to keep him busy on “special projects” to suit the boss’s politicking
A lovable rogue antique dealer with his heart in the right place gets into scrapes while solving other people’s problems. [His aristocratic not-quite-love interest is played by Phyllis Logan, whom you might recognise from Downton Abbey]
More recently Shakespeare and Hathaway
Private detectives in Stratford, whose cases carry more than a few faint echoes of the Bard. Have fun spotting the quotes!
If you like nice little shows that reference Shakespeare, try to find Slings&Arrows, a Canadian production. Three seasons, each self-contained, no cliffhangers.
Slings & Arrows centers around life at a fictional Shakespearean theatre festival in New Burbage, Canada. Each season focuses on The New Burbage Festival’s production of a different play. The themes of the play are often juxtaposed with personal and professional conflicts facing the festival’s cast and crew.
Slings & Arrows was excellent.
I’ll keep an eye out for it. Looks like I might find it on YouTube (avoiding too many subscriptions!
Have you read any of the books by Jonathan Gash that this series is based on? While I enjoyed the shows, I found the books so much richer, and very scathing towards almost everyone involved in the antiques market. Apparently the author worked in several antiques markets in London while he was studying medicine, so had first-hand experience of the shady practices so evident in the novels and the TV series.