Ask your DM
Dan B already laid out the main point: there are no explicit rules about this, and the two statements contradict each other, so your DM will have to make a call.
But what is a good ruling here?
Allowing this is unlikely to cause problems, and it feels petty and unfun to not give a character whose stick it is to speak to plants and beasts the ability to also do so when they use telepathy. It should be OK to allow them to work together.
Here are a couple of additonal considerations:
Power of Telepathy in the game
Other forms of telepathy are more powerful, for example the spell Telepathy
The spell enables a creature with an Intelligence score of at least 1 to understand the meaning of your words and take in the scope of any sensory messages you send to it.
The feat could have easily used this formulation (and match that of the racial ability), but instead is more limited. The feat otherwise would give you the equivalent of a permanent 8th level spell with proficiency in all languages, which would be much more powerful and also allow you to speak to anything with any intelligence. For comparison, the Linguist "half-feat" gives you access to only 3 languages.
So, to keep the feat balanced, the designers were forced to use a formulation that is creating the mismatch in wording here.
Languages of Beasts and Plants
The limitation in the feat does two things:
- you cannot speak to creatures that only speak another language just because you are Telepathic
- you cannot speak creatures that have no language at all, just because you are Telephathic
The second is the exact limitation that Speach of Beast and Leaf overcomes, and it seems reasonable that it should also overcome it in this context.
Most plants and animals are too dumb to know any language. Look for example at the Shambling Mound, a plant monster:
Because most plants have no language, the Speech of Beast and Leaf cannot be worded to enable you to speak in their language, it needs to be worded differently.
Intelligence limits on communication
The main disbelief to overcome when speaking with things like insects or plants is that they lack the required intelligence to understand what you are telling them or to tell you anything coherent.
What could a plant with likely 0 or 1 Intelligence and very limited sensory organs even tell you? That the sun feels warm and nourishing on its surface?
Your DM needs to decide how they want to handle this. Are they limiting your communication to just what the creatures can percieve and reason, which would make it pretty useless in the case of most plants, and much weaker (but possibly an entertaining roleplaying challenge) for most animals? Or will they decide it instead is rather something akin to the fox in Tolkien's Fellowship of The Ring:
A fox passing through the wood on business of his own stopped several minutes and sniffed. "Hobbits!" he thought. "Well, what next? I have heard of strange doings in this land, but I have seldom heard of a hobbit sleeping out of doors under a tree. Three of them! There's something might queer behind this." He was quite right, but he never found out more about this.
The question if you can meaningfully communicate with dumb animals and plants is more fundamental, than the question if you need to understand their language to do so. If the DM allows it, than they also should allow it when doing it silently.