In this context forthcoming means "about to happen", "about to appear", or "approaching in time", but it doesn't denote a specific time frame. It could be hours, days, or months.
The nature of a particular event may imply a time frame, for example if I said something about "our forthcoming meal", presumably we would be eating within a couple of hours, not next month. If I said something about "our forthcoming baby" that could still be a few months away, but not more than eight months away (assuming the pregnancy was confirmed after one month). If we're already sitting in the audience then the "forthcoming performance" of a play might be just minutes away.
This piece of music is from my forthcoming album.
Some decades ago musical albums were recorded in a matter of days or weeks, but these days many artists take months to complete the recording process - more than a year in some cases. Once recorded, an album won't actually be available for sale until the cover artwork is complete, CDs have been manufactured and shipped to shops, MP3s have been lined up for download, etc. So a "forthcoming album" may not be due for a few months. Or it could be due next week. Some artists don't release CDs, they only do MP3s online, so their albums can be made available more quickly. From that one sentence we can't tell, though I would assume production is well underway or nearly complete.
How can I view my Forthcoming Projects?
Without knowing the nature of the projects we really can't tell how long it will be until they happen. In some fields an individual project may take months. In some fields an individual project may take days. Forthcoming projects presumably will happen after current projects have been completed.