I love Anakin and Yoda being friends
As strict as Yoda can be I think he genuinely enjoys having someone like Anakin around. Like Qui-Gon, Anakin is somewhat of a maverick within the Order and I think part of Yoda appreciates those Jedi who are willing to bend the rules somewhat as they're certainly far more interesting to him than the ones that fully commit to the dogma of the Order and never really stray from the rules.
And for Anakin's part him having a friendship with Yoda further adds to the tragedy of his fall. Anakin really had great support from within the Order (Yoda, Obi-Wan, Ahsoka, etc) but in the end his faith gets burned too many times by the Order throughout the war to the point where he felt Palpatine was the only one he could trust. And despite never actually being Yoda's Padawan it has to hurt that this is the second Jedi who Yoda was close to that got lost to the dark side after Dooku (that we know of anyway. A lot can happen in 900 years.)