I'm struggling to get the recommended amount of protein while still staying at my calorie limit.

That's likely more protein than you need. Protein is needed to maintain our lean tissue: We don't need a bunch extra if we have some extra body fat. The problem is that most of us may not know our lean body mass very accurately.

It's more than the USDA recommendation, but quite a few of us here (me included) think that 0.6-0.8 grams per day per pound of healthy goal weight is a reasonable minimum. If you don't have a definite goal weight, use the middle of the normal BMI range for your height.

Another option is this evidence based protein needs calculator:

https://examine.com/nutrition/protein-intake-calculator/

It's from a site that's generally regarded as neutral (for example, they don't sell supplements!). The background information about their recommendations, including citing relevant research, is here:

https://examine.com/guides/protein-intake/

I'm a vegetarian myself, though ovo-lacto, and have been vegetarian for 47+ years. It does take a little thought to get adequate protein on lower calories, as a vegetarian/vegan, but it's possible.

In case you haven't run across it, this is a good site on vegan nutrition, run by registered dietitians and science-based:

https://veganhealth.org/

They have good info for new vegans, how to get some of the nutrients that require extra attention, etc.

My personal tips are to think in terms not just of "one big protein per meal", which is often the way omnivores plan eating ("what's for dinner?" "chicken"). Of course, one major calorie-efficient protein contributor in every meal is still a good idea (tofu, tempeh, edamame pasta, seitain, other legumes, etc.).

In addition to that, think in terms of getting a little protein in most things you eat, when possible, rather than choosing things that have no protein at all. For example, for a little crunch and some healthy fats on a salad, I'd use a sprinkle of nuts or seeds rather than croutons or oil (I often use just seasoned vinegar as a dressing, plus the nuts/seeds). Frequently choose veggies that have a little protein (broccoli, spinach, many more) over those that have nearly none. Use calorie-efficient seasonings like nutritional yeast, peanut butter powder or almond butter powder, miso, etc., that add flavor plus a bit of protein. There are snacks with more protein than others (dry-roasted soybeans, crispy broad beans or chickpeas are some examples). Even some fruits have a little protein, like guavas.

A good place to identify some of those things is this thread, here on MFP:

http://community.myfitnesspal.com/en/discussion/10247171/carbs-and-fats-are-cheap-heres-a-guide-to-getting-your-proteins-worth-fiber-also

That lists many, many foods in order by protein efficiency, most protein for fewest calories. You'll need to scroll past the mostly meaty/fishy foods nearest the top of the list, but there are plant sources further down. I found that spreadsheet really helpful when I was trying to get more protein on fewer calories.

When I was losing weight, I was able to get to the 0.6-0.8 grams per pound of goal weight range quite consistently, eating 1400-1600 base calories plus exercise calories. For me, as a 5'5" woman with a goal weight around 125 pounds (I have a narrow build), that's 75-100 grams. I think most days while losing I was getting grams in the 80s-90s generally.

Now, in maintenance, I'm eating 1850+exercise most days, targeting 100g minimum, and exceeding that quite routinely. I admit, I do eat quite a lot of dairy (my Northern European genes handle it well, and I like it), but not all that many eggs. However, I eat enough plant foods that I'm pretty sure I could get to that protein level eating fully plant-based. To do it, I'd probably have to eat more soy foods than I really prefer, but that's a taste preference thing, not a health issue for me. I consider traditional soy foods to be nutritious and helpful - also tasty, but maybe not multiple times a day. YMMV.

It's your calorie level that directly matters for weight loss, though nutrition generally can have an indirect effect through things like energy level or cravings. Getting enough protein is useful as one part of avoiding unnecessarily large amounts of lean-tissue loss while losing fat. It's not something that needs to be perfect immediately, you can work at upping it gradually.

Unless you object to it for some reason, one option would be to use a vegan protein powder (in smoothies, shakes, or cooked foods, etc.) as one piece of getting the protein level you want, alongside gradually increasing protein from other foods (if you prefer getting protein from food vs. a supplement - I do, but again that's more taste preference than any kind of grand philosophy on my part).

Best wishes!

ETA P.S. If you want to see what I eat, for ideas, my diary is open to MFP friends, and you're welcome to send me a friend request if you want to see it. I don't log every single day anymore (I'm in year 6+ of maintaining weight), but do log most days. I'm a sub-par MFP friend, but will answer food questions on my timeline or by PM.