No, I don't think he's afraid of Putin, but I do think he's really unsure about how to confront him. If he's afraid of anything, it's that he's afraid of misreading the situation and making a catastrophic mistake, either by being too soft or by being too aggressive. Biden is just being Biden. He's aiming for the middle ground. He's going by the book. He's being measured. He's not really showing a willingness to take risks or gamble, and that's the way he's always been.
When the people in the situation room had a chance to take out Bin Laden back in 2011, Biden was among those who opposed it. It was not because he was afraid of Bin Laden, but he was afraid of repeating another major intelligence mistake (he got burned for supporting the nat'l security assessment leading up to the invasion of Iraq, you may remember). He was afraid of getting Navy SEALS killed in Pakistan, killing civilians in a neutral 'allied' country, and deteriorating relations with Pakistan. So he opposed it. Obama, however, is someone who occasionally is willing to put a big bet down on the table, and so Obama went for it. And as it turned out, Obama was right and Biden was wrong.
But Biden does Biden, and here the stakes are much, much higher. This is pretty much what I'd expect. Biden is cautious -- you could argue he's being too cautious. For the record, I think he is being too cautious right now. But at the same time, don't confuse cautious with being afraid or scared. I don't think he's afraid of Putin. There's actually a lot of risk in choking Russia's economy the way we have, as it puts tremendous pressure on the regime's long-term survival. That actually does take some courage, because these sanctions have real consequences, and those consequences are already making Russia's regime feel pressure and frustration. It took courage for Biden to push for these harsh sanctions. It also takes the ability to build and coordinate alliances, which is something that Biden does exceptionally well, whether it's working in domestic or international politics.
Tl/dr: Yes, Biden's being too cautious, and is worried about making a big mistake, but no, he's not afraid of Putin.