Question:
Why does China doesn't consider itself to be a member of the G77 while the G77 itself lists China as one of its members?
Short Answer
Power politics and competition. The U.S. is a leader in the G7, the middle powers have greater sway over the G20, and China leads the G77. As you say, by both being a member and not being a member the G77 is called the "G77 + China". It's like it's their club, an impression they work hard diplomatically and economically to promote.
Background
The G77 made up of 135 countries, 80% of the worlds population. It's members are mostly developing countries. These countries are very important to China. China's vision of a multi polar world is dependent on forming economic relationships with developing countries, the more exclusive the better. This is the same rational for China's leadership in forming the BRICS group. The vision is over time a broad alliance of developing countries could make China less dependent on the G-7 for trade. Even displace the G-7 altogether. This makes sense as China itself was considered a developing country just a decade ago and today they're one of the largest economies in the would. In 1970s the G-7 countries contained 67% of global GDP, today it's only 30%.
G77+China summit in Cuba seeks to strengthen voice of 'global South
As UN Secretary General Antonio Guterres, who attended the summit, said: “This multiplicity of summits [i.e., BRICS, G7, G20, G77, ASEAN, etc.] reflects the growing multipolarity of our world.”
So why is China both a member and not a member of the G77.
If China was a member we would simple call it the G77. Since China is both recognized as a member by the group, but claims not to be a member; the group's official name and official statements are the "G77 and China". It gives China all the benefits of membership plus the added benefit of being separate and above the rest of the members. It diplomatically advantageous.
despite being politically aligned with the G77 and providing them with ample political and financial support?
China leverages the G77 for it's own means. Like rallying support for its Belt and Road Initiative (BRI), Shanghai Cooperation Organization (SCO), and BRICS. It promotes solidarity to resist the current world order to replace it with a more China centric globalist model.
Overall it serves the poorest nations because the wealthier countries in the G77, such as China, India, South Africa, and OPEC; bring with them experienced negotiators and stronger political status. On the negative side, when there are competing priorities; global warming for instance. Issues which pit poorer countries interests against those of more developed members. China and OPEC nations are economically dependent on fossil fuels. The G77 tends to struggle on important issues for developing nations which don't reflect it's wealthier member's interests.