How to transform an imbalanced attribute to make it more suitable for linear regression?
You have multiple options and you may choose the best by seeing the performance.

First one is to use a guess. For positive-only values the log-transform is a hot candidate to make sense (maybe correct for small values here to avoid exceedingly large negative transformed values).

Log-transform is natural if percentage increases have a particular real-world meaning. This is often the case for financial data. Why is log a hot candidate? You probably know that when there are addititve real world effects, the normal distribution often appears. Now, when you have multiplicative effects, you get the https://en.wikipedia.org/wiki/Log-normal_distribution .

Other common transformations are power transforms, where you take some power of the values. I don't think there are many more which are very common. Theoretically, your perfect transform would make the noise on the linear regression Gaussian, but no-one can tell what that would be and most likely reality isn't perfectly linear anyway.

A transform is more interesting when the transformed values follow a Gaussian distribution. But that is just a guess and in the end only final performance evaluation can tell more.

For a second option, be aware that you can force the transformed values to be any distribution you want. For example, if you take ranks of the values you get a uniform transformed distribution. You could even force it to be a Gaussian by a suitable mapping. However, in your case, this will lose the interesting bump on the right.

I think these are the most common options. In data science, nothing is ever obvious and most of the time you can only decide by performance evaluation (cross-validation with the whole model).

Conclusion:

Set up a performance test (cross-validation; not on final test set though if you like a fair, final evaluation) and try all of the following


Try untransformed. It might already be what has most information.
Try log-transform (while adding a small offset if you have some very small values)
Try power-transform if you like