Does increasing value of a still-out-of-the-money option that you wrote (covered) pose a risk to you?

You did not indicate what overall strategy you are employing and that determines the answer.

If this is a covered call, there are no consequences if implied volatility increases. The risks that a covered call writer face are opportunity risk (the call is assigned and you miss out on the security's gain above the strike price) and the asymmetric risk of receiving a small premium while bearing all of the downside risk of stock ownership (less the premium received).

If this is a naked call then not only do you face unbounded upside risk but your margin requirement can increase significantly due to share price change.

If the price of the contracts rise, it's a "paper loss", meaning a position you hold has incurred a loss, but it isn't locked in unless you make a transaction. If you were to close the position in that exact moment, then of course you would incur losses. But if you hold out long enough or eventually to expiration, the price will eventually approach zero and become worthless at expiration.

So, there is no other risk to worry about, except for the position expiring while ITM.