All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
In principle, the contract is the law between the contracting parties, and the conditions agreed upon by the parties in the contract must be adhered to, provided they do not involve anything prohibited. The Prophet Mohammad (peace be upon him) said: "Muslims are bound by their conditions except a condition that forbids what is lawful." (Reported by Al-Hakim).
Framing the scenario mentioned in the question between the teacher and the platform owner as a business partnership, where they agree on specific tasks and distribute profits according to a pre-agreed percentage, can be considered akin to a "partnership in industries" or "partnership in acceptance." According to Imam al-Marghinani, a Hanafi jurist, such partnerships, where individuals collaborate on tasks and share the earnings, are permissible. He stated: "As for a partnership in industries, also known as a partnership in acceptance, like tailors and dyers who collaborate in accepting tasks, and the profit is shared between them; this is permissible." [Al-Hidayah, Sharh al-Bidaya, Vol. 3/P. 11].
If each partner performs their designated tasks, each is entitled to their share of the profit. However, if one partner takes on the work and compensates for the shortcomings of the other partner, they are not entitled to an increase beyond their agreed-upon share of the profit, unless it was stipulated otherwise. If an increase in the profit share was not specified, the partner who contributed more would be considered as making a donation. Imam al-Kasani, a Hanafi jurist, stated: "Whether they work together or one of them works without the other, the profit between them is based on the agreement because entitlement to profit in the partnership is based on the condition of work, not the mere existence of work." [Bada'i al-Sana'i, Vol. 6/P. 62].
In a partnership, it is not permissible for a partner to work independently for their personal benefit because the partnership contract is based on trust among the partners. However, if one partner wishes to work independently, they must first terminate the partnership contract.
In conclusion, the teacher who takes on the responsibilities of the platform owner is not entitled to anything beyond the agreed-upon profit in the contract. If the teacher wishes to work independently, they must first terminate the partnership contract with the platform owner and then proceed to work on their own afterward. And Allah the Almighty knows best.