You could take your camera to a camera shop and ask them if they could try it with another lens for you to see if it's the camera or the lens that's got the issue. Then you might be able to buy another lens (used or new) from the camera shop and be back in business again for not too much money. Or (and now I'm probably going to upset some people here, but what the heck!) if it won't strain you financially or put you in debt, and you want to take this opportunity to upgrade your gear, then you could perhaps get something like the Canon 6D and an L-series Canon lens?
Yes, you
can get good results from your existing camera/lens set up, but you may have to work a bit harder to get them. I upgraded to a Canon 6D three years ago from a Canon 400D (I know that was a big upgrade in terms of years and spec, but hear me out). I could get good looking images from the 400D, particularly when the lighting conditions were favourable, but I was amazed by how much better the images looked straight from the camera with the 6D. Particularly in sub-optimal lighting conditions, and also with a dedicated Canon Speedlite flash (a 430EX II, I think). If I wish, I can put the thing in full auto, press the shutter and get a well-exposed, lovely-looking shot almost every single time.
So yes, you
can get good-looking results from a cheaper camera and lens, if you work at it and get the lighting right, etc., but I find the 6D makes a real difference in borderline or difficult lighting conditions. Plus, I found I can get some nicer looking bokeh/shallower depth of field from a full frame camera, if I want it. So weigh up your options and finances carefully; you may well be able to carry on with your existing camera if it's just the lens... or you may decide to trade the camera body in (if it works) against an upgrade. As long as you aren't going to overstretch your finances there is nothing wrong with wanting a more advanced camera, providing you can genuinely use the benefits it may bring.
The Canon 6D Mk1 would be more than up to the job of photographing those objects in your photos, and the images I saw when I clicked the first page of the cookery website you linked to. I find the images from the 6D Mk 1 tend to look very nice straight from the camera as JPEGs too, so that might possibly save you a bit of time in Photoshop. So I don't think you need to go to the expense of a 5D III or a 6D Mk II (so watch you don't get talked into that by a sales person!), as I said previously, the low light/higher ISO performance of the 6D is considered to be better than the 5D Mk III too, so it could actually be better for the natural light shots you take? Weigh up your options and see what you think.
As for a lens, if those shots are typical of what you do and need, then perhaps think about a Canon 24-70 L (either the f2.8 or the f4 IS) if you can find a good, mint,
latest version of one of those
second hand via a reputable dealer with a long warranty? They are more expensive than the EF 24-105 L IS Mk 1, but they are meant to be a bit sharper. If you always shoot using a tripod then the Image Stabilisation option might be less appealing to you, and the additional bokeh the f2.8 might give may be more useful? Once again, do some internet research, look at some examples of the images from each of these lenses and see what you think would suit you the best.
If your existing camera body works and just needs a new lens then
do think carefully about upgrading, you'll probably have to sell a lot of cookware to make enough profit to pay for a Canon full frame camera and L series lens (even a good, used one) so don't let your heart rule your head! Best of luck deciding on what's best for you, and I hope the above suggestions are useful.