I am developing a website and want to list the logos of the
technologies I used in the footer. [...] My question is, am I allowed
to do so, or am I restricted to use only those formats that were
supplied by them.
The relevant areas of law here are (at least):
- copyright law
- trademark law
Copyright law says that (almost) any use of a protected work (or a work based on it) requires permission of the copyright holder. This certainly includes putting the images on your website. People get sued and pay huge sums for putting images on the web without permission.
So the first thing is: You need the copyright holder's permission to post any image in any form. If you intend to modify the image, you will need express permission to do that, too (in addition to the permission to use it in the first place). Now, strictly speaking, a mere conversion to a different file format may or may not count as a modification in the copyright sense (as the image still looks the same), but I wouldn't risk it.
In addition to copyright law, posting an image that serves as a company logo could get you in trouble with trademark law. Details vary a lot between jurisdictions, but basically: If you use the logo in a way that could imply that you are affiliated to the company or endorsed by them, that could land you in trouble. Again, to be on the safe side, you need explicit, written permission to use the logo.
In the case of trademark law, there are arguably more exceptions than with copyright law - for example, use of the logo is usually allowed if you make it clear you are only reporting on the company. But that is tricky to get right, so be careful.
To address your specific case:
- You will need each company's permission to use their logos. They will tell you exactly what you may or may not do.
- Many companies actually want you to display their logo. These companies will often have a page with logos you can use. For example, MongoDB has a page Brand Resources with logos. If such a page exists (and it really is from the company), then that is usually sufficent permission to use the logo. However, the page will usually state conditions for use (such as no modifications) - you must follow these conditions.