The most complete edition of the State Trials is that by Cobbett and Howell. Links to the all 33 volumes on Google were diligently compiled by Naomi Clifford, but when that site went down I scraped the links and put them below. Another set was hosted by the seemingly defunct Constitution Society, but can be found via the Wayback Machine. Hathi Trust also has a complete set, with multiple doubles.
A preceding compilation, ‘A Complete Collection of State-Trials, and Proceedings For High-Treason’, (6 volumes, 3rd edition, 1742) was also hosted by the Constitution Society, in chunked pdfs of 50 pages each, and again can be found via the Wayback Machine. The Internet Archive has this set, with the four additional volumes, the last published in 1766. The second edition (6 vols, 1730) of this can be found on Hathi Trust.
Lushington’s two volume selection is available in transcribed text at Project Gutenberg: [vol. 1] [vol. 2]
There was an 8 volume continuation, the State Trials New Series, that covered the period 1820 to 1853. All volumes are available through Hathi Trust, and Wikipedia has links to the Internet Archive’s copies,
Cobbett’s State Trials
Volume 30, 1822, 1806-1808 (1822)