My impression is that the English well-to-do were very legalistic-minded in the 19th century, and Georgina's father would have this in mind when he made the provision for Georgina. Provisions in will require clear words to be legally binding and "precatory words" or recommendations were not legally binding. For instance, Wickham told Eliz that the late Mr Darcy left the Kympton living to him but when Eliz read Darcy's letter that his father "in his will he particularly recommended it to me, to promote his advancement in the best manner that his profession might allow -- and if he took orders, desired that a valuable family living might be his as soon as it became vacant." -- Eliz felt that "the difference was great. What Wickham had said of the living was fresh in her memory ... it was impossible not to feel that there was gross duplicity [legal bequest or recommendation] on one side or the other; and, for a few moments, she flattered herself that her wishes did not err [i.e that her wishes that Wickham was telling the truth, and that Darcy was lying ]. But when she read ... of Wickham's resigning all pretensions to the living, of his receiving in lieu so considerable a sum as three thousand pounds ..."
Georgina's 30,000 pounds might have been her mother's marriage settlement, or part of it could have her mother's marriage settlement and part of it added from her father. Of course Darcy could add to his sister's fortune later if he wanted to, especially for instance if she married someone he liked but who was not very rich, but he was not legally obliged to do so. If he did, it would be purely out of his generosity and the goodness of his heart. Her 30,000 pounds was what was legally hers, no more and no less. In S&S, the Norland estate was tied up for the benefit of John Dashwood's son on Mr Dashwood's widow and daughters were left with only 10,000 pounds for their provision. As John Dashwood was rich -- he had his late mother's fortune, his wife's dowry and the Norland estate for his lifetime -- Mr Dashwood hoped he would add to his half-sisters' small provision, and he promised to do so, but he was not legally bound to do it, and in the end he gave them nothing at all. And Darcy himself was quite young at that time, only quite recently of age, there was no guarantee that he would not marry a Fanny Dashwood-type who would persuade him not to do give anything to his sister. Old Mr Darcy also left Georgina to the joint guardianship of Darcy and Col Fitz, as though he was not completely confident that young Darcy on his own would be a sufficiently good guardian.
Georgina's 30,000 pounds might have been her mother's marriage settlement, or part of it could have her mother's marriage settlement and part of it added from her father. Of course Darcy could add to his sister's fortune later if he wanted to, especially for instance if she married someone he liked but who was not very rich, but he was not legally obliged to do so. If he did, it would be purely out of his generosity and the goodness of his heart. Her 30,000 pounds was what was legally hers, no more and no less. In S&S, the Norland estate was tied up for the benefit of John Dashwood's son on Mr Dashwood's widow and daughters were left with only 10,000 pounds for their provision. As John Dashwood was rich -- he had his late mother's fortune, his wife's dowry and the Norland estate for his lifetime -- Mr Dashwood hoped he would add to his half-sisters' small provision, and he promised to do so, but he was not legally bound to do it, and in the end he gave them nothing at all. And Darcy himself was quite young at that time, only quite recently of age, there was no guarantee that he would not marry a Fanny Dashwood-type who would persuade him not to do give anything to his sister. Old Mr Darcy also left Georgina to the joint guardianship of Darcy and Col Fitz, as though he was not completely confident that young Darcy on his own would be a sufficiently good guardian.