Just tried it with Gboard with the "Sanskrit" keyboard layout.
For "क्" -- first choose क (in the top-left). In the bottom-left, you'll see the half क्
For typing "बुद्धि" -- first choose ब then choose बु then choose द then choose द् (in the bottom-left, as with क् above), then choose ध, then choose द्धि
(It does not seem very convenient, but maybe one can get used to it.)
The other alternative is the "abc -> संस्कृतम्" keyboard layout, where one can type (using a QWERTY keyboard) "buddhi" and hope to get the correct output बुद्धि (usually works for common words).