1 ACCEPTED SOLUTION
In the following opinions, I have and use all of the lenses I recommend, except for the Tamron, but it has an equally good reputation compared to the Sigma. I have provided images and links to offer some extra information.
Given you have advised a budget of $700-800, you might be able to get a used Tamron, or Sigma 150-600 Contemporary lens on the second-hand market as some folks relinquish their EF glass in favour of RF lenses for the Canon R-series Mirrorless Interchangeable Lens Camera Systems (MILCS). Either of these is a great optic, but will leave you with a 100mm gap in your focal range between that and the 18-55.
Alternatively, another unit to consider is the Canon EF 70-300 IS USM f/4.5-5.6. As you apparently understand the principle of crop factor, this will render a Field of View (FoV) equivalent to 112-480mm on a Full-Frame camera. The MkII version is an excellent optic: fast focus, good image stabilization and not too heavy for your 4000D camera body.
There is one available from the Canon Refurbished site, where lenses have been serviced to essentially new condition, and come with a 3-month warranty. Here is a link to one for sale on that site, and it is well within budget. I have produced a review of 70-300mm Canon lenses and if you are helpful, you will find it Here .
If such a lens was acceptable, then you would have some budget left to replace the 18-55 that you are not keen on, in which case the EF-S 18-135 IS STM or IS USM would be great options, and they are reasonably cheap. They have a much wider focal range and are a better optic all round than the 18-55 you likely have.
If you are prepared to wait a while and find a few more dollars, another excellent lens is the Canon EF-S 15-85mm, which would combine nicely with the 70-300. The extra 3mm on the wide angle end makes a considerable difference when shooting indoors, for example. It is an excellent optic, and has been called the secret L-lens for it's quality of images. 
In the sample image above, the street is on an incline.
I hope you will find this information of some value and encourage you to ask further questions as you need to.
For Wandalynn:
Is this something that you are asking for yourself? As I observe you seem to specialize in close-up imagery, I would suggest the addition of a set of automatic extension tubes to give you a much larger image with any lens that you have. I stumbled upon this video just after writing this as I have the Sigma 60-600, but it refers to the use of extension tubes, so have included this for added information. If you go to timestamp 7:23 in the video you will see a demonstration of the use of extension tubes - just ignore all the stuff about focus breathing per se.
Sigma 60-600 vs Sony 200-600: BEST WILDLIFE ZOOM LENS! - YouTube
For the OP
We don't know that the OP's definition of wildlife covers very small objects close up. In any case, if it is critical, I would expect that they would look that up in the specs. As the OP's combination of wildlife and landscapes is a wide one, it is hard to find a single lens that is capable of both, especially if one is then extending that definition into close-up photography. By close-up photography I do not include macro capability in its strictest sense.
In the OP's case, it is for that reason that I suggested two lenses: the EF-S 18-135 IS STM or USM, and the EF 70-300 MkII. While they each have a range that is complementary, with some degree of overlap, they are both reasonably capable of getting close-up shots. For example: these images are taken as indicated with the two different lenses, hand-held in available light.
In this image the subject is about 2.5cm (1") in diameter, so I think that would qualify.
The other criteria of the OP we know is budget, and that lens combination would likely be within, or very close to the $800 maximum specified. One of the most important criteria is what is going to be produced, and while that is not specified, it is unlikely that the OP is going to attempt large, detailed prints - especially with a Canon 4000D. Most likely we are looking at output on digital devices - either monitors or via social media - where both of these lenses are quite capable of generating acceptable results. For example on this site, the resultant images are drastically reduced in resolution.
