The half notes here suit vibrato.
Vibrato in general is a big topic, and there are many experts with widely varying opinions.
Your teacher will be a big help. A nice vibrato takes time.
Generally bass vibrato is from the arm, it is not a hand vibrato. Lower notes and softer intensity suits a slower vibrato, with faster vibrato for high notes and intensity. It can be effective to start the note with no vibrato then come on strong Gary Karr style.
There are singers who have a vibrato/sound I love and I try to copy them. For myself, Nat King Cole comes to mind even when I’m playing classical.
Orin O’Brien feels there is no place for vibrato in classical pizz, but I have had conductors request a big vibrato on the pizz. Some jazz bass players feel there is no place for vibrato on pizz. You get to make up your own mind. Baroque players have opinions on vibrato use.
With treble clef sometimes I play an octave down pizz, when comfy an octave higher pizz, and finally with the bow. It’s a process. Don’t avoid treble clef as it can be a block later. Ironically tp playing is considered easier by some than the lower positions. High position playing and crossing strings vs shifting gets comfortable with short regular practice doses.