Pieter Wuille has answered the technical question of how these transactions are affected by the rules.
Vojtěch Strnad identified the origin as Ordinals Inscriptions - a kind of NFT.
When I asked "will it affect the size of the UTXO set?", I was also interested in the overall effect on Bitcoin ...
In January, I wrote a program to look for witness components larger than 1000 bytes in recent blocks and found 55 of them. The latest "Inscription" on the Ordinals.com Inscriptions page was "Number 81". I was short because some inscriptions are just a short URL or a tiny image and are smaller than 1000 bytes.
Tx 26482871F33F1051F450F2DA9AF275794C0B5F1C61EBF35E4467FB42C2813403 W1 C2 20437 bytes
Tx C17DD02A7F216F4B438AB1A303F518ABFC4D4D01DCFF8F023CF87C4403CB54CA W1 C2 9480 bytes
Tx 22D7FA836A87E0532E9AFF8D29A1B0AA872CE45545E55D9D9C73CB4309FC8BC3 W1 C2 5553 bytes
Tx A4B5580DB345DB7534B74371F40562BA0D6F79FD272E05C62C05DB1B62996D23 W1 C2 34393 bytes
Tx D95C0FB86BC0F0DCE6A732C5AB77D47E33ED24099BDB01133F768CEF75A47724 W1 C2 28650 bytes
Tx 7460A1068F98E1FAC798304ADDCA4B5EED1CC9968CD5526E07C2CEB3EC7CF7B3 W1 C2 49970 bytes
Tx 7641EF7165BC59C40B269D4B2F6741CA3F34334B8C758FBBA155BD0E29B4011B W1 C2 104169 bytes
Tx 16F3C32468E3E52AC20DC8FC633C686F0E31C5F34407413D12AD764BA5AD5F3B W1 C2 71832 bytes
Tx 517EE232143D289D70867F88CBE2B9B161EF56554BC4FA7796E672D41E2E2BF3 W1 C2 37718 bytes
Tx F04DD50561899F650103703526A62BC2510CD1B2F185F02E76936314AF42A145 W1 C2 60034 bytes
Tx A6628F32A5B41B359CFE4AB038FF7C4279118FF601B9ECA85ECA8A64763DB40C W1 C2 73433 bytes
Tx 31833061114C2EE53D63DBA53EF0BC2AF741C87463CF573A4E211196883A5F2D W1 C2 245308 bytes
Tx 9163AF650DCDEEEB9A7E1F47F693B51921DCE3BDF2475E69360EC83D9956F5D7 W1 C2 2692 bytes
Tx CA009BF4CAE18D22444C7A31FB05AB372816CDBFBB3FD741812DCA674ADF0CB5 W1 C2 6821 bytes
Tx FD5B77F56C2B785F7266143E1DCD8B83B82050CEB7D2D7344AA3999F3CC17D4D W1 C2 76022 bytes
Tx 0C107942E4C945B6B44E193C950B0FAE65D854A88B450758A3FCA54017C879BE W1 C2 55261 bytes
Tx 9905C43CABE642666E43BD1C059D9093B96204330A2EEB33AC22B7142B1D57ED W1 C2 24745 bytes
Tx ADC408A32E887777007C145DA9CFAFDA88B88917E15D06E4B0097C31CD38AB11 W1 C2 2628 bytes
Tx 562CD1136399F7A6568F41081F85C88145B87E7E70A3A53748A46902E6B84D60 W1 C2 2682 bytes
Tx B375BCCE16C91F3DEF7871933F1696DD3681199E0F23E90D980A87DBF57E6699 W1 C2 2646 bytes
Tx 1FDBD2BBABFAA9B64BBD529D5A2D5FB1B39FFCBDD6C39601BEAAC5E3260C9FCE W1 C2 2728 bytes
Tx 7B68ACED40476A4CAEDB2A5D014974C522331291B6A78BED06BBC891CBE14C9B W1 C2 96909 bytes
Tx 9D0AD29EF2923DF9D598A1A890EAD36EBBE44F1F1D77D93EFA21325806311F28 W1 C2 360490 bytes
Tx 03A6381C7E224D4FE2425B5F5DA3782E8BD5701E783BD0AF4EE1E2700DBBB347 W1 C2 269502 bytes
Tx B8BF03E34F8FB497941A878793F7138AAB502F4A34604923CC3147EF7F6BA471 W1 C2 2702 bytes
Tx 372284D650D297F53309D790CF173D1FC5C2EE4D90250CEE76C6A574EC69882F W1 C2 5345 bytes
Tx 239882AB23041B1F017E19174F24E6397EF10A295484F395D550CAAA61239B8D W1 C2 1907 bytes
Tx 7ECCD70601A5A65421F560743F2661116BC88B4D73A72F4199850B498CE8E996 W1 C2 245062 bytes
Tx 5166A9EF575565ED67D63044FC442A8EF07B4AD20631442D477F784B4CB1BD29 W1 C2 2677 bytes
Tx 6B76932BB8F2478FE58D27B9F80C1C6D02AC0083BA34F9F46A2A171E9A385851 W1 C2 201956 bytes
Tx 40B3279C70D31B1C53D430A245EC012DABF173A47384F33E54DB34E8E7732570 W1 C2 2715 bytes
Tx 913D65CA95AFD862A71FEA8D48CF95434EFD3581B8D08D3F0402DB526D975EFA W1 C2 101461 bytes
Tx 8D9933F3C5BA17025B69FBCBF136EE237320125448E02C2EB1045286879955D5 W1 C2 45629 bytes
Tx E9B1379E9A30E4E2F08FA0C38394F49AA0B92449423F966C6108BE93533C17B6 W1 C2 6979 bytes
Tx 5E1BA5C92673452E3422A553BF641CD634B46FC28FA27ECABFFC917039DE1869 W1 C2 2741 bytes
Tx 1AA4F606890680A9B381BA4E9130894288DD21336B82CBFD75DC19DB38ECE937 W1 C2 2654 bytes
Tx CFAB194B924F7785C6E453728E1C264B89B74843633278CDA3AD3F57576C1E93 W1 C2 51196 bytes
Tx 69908239157F1E069FA3A0469BAD21B49187823D18E729D1EBE29B9252F5BD98 W1 C2 14753 bytes
Tx E3E29332B269D0AE3FA28AC80427065D31B75F2C92BAA729A3F8DE363A0D66F6 W1 C2 28597 bytes
Tx 54E47C2F0E75142D1D7A0FE585E81ACEB8759B07C6CFE9FA1A0BD6C317EAE8B3 W1 C2 37099 bytes
Tx 8A3E28442DEC1E4C56133F75000778121BFE46ECD9FC1C447F8A8315D01017C9 W1 C2 2699 bytes
Tx 36E0C45C1476F059E0A990B5358DA3C3ED9E15F6BBD12AFF5C955A009B65AA5F W1 C2 1077 bytes
Tx 94C7DF559AF3CE875ED49375D8F199B30735D580AD102B920F70B74BAAD17801 W1 C2 4137 bytes
Tx AB2F4E9DCE0583264078428A91AA9037DA0E75F90DC77FE3CBA7CF5320AD003D W1 C2 29518 bytes
Tx 87295FF96556BC668C44068875AED32FBBBCEBB8D5AF3869FE37B264BA319A00 W1 C2 5023 bytes
Tx 85B10531435304CBE47D268106B58B57A4416C76573D4B50FA544432597AD670 W1 C2 185416 bytes
Tx 5A16C5BF8BBCDF978AF8BF511D9AC71CC6E4457F694F4F7ED499F4C8E18EDF79 W1 C2 60199 bytes
Tx 0BD542EC42B205332C4C00739A83C7342BF4F435CAFD569EB543B00E62A852FD W1 C2 126091 bytes
Tx BD0731B218B77A6F2EDA6FCD64FC00305686A38DD474B4D5341BF57945899559 W1 C2 96318 bytes
Tx 2999656AA17255CB9944AAD1B0853937C0BDBC595120E5A5FA97F622ED302AEC W1 C2 128809 bytes
Tx FDCF0B5725301493F3BBB0564D9A1ECAC9AB5BAA0D3C6523CA77186184F3C3FA W1 C2 160042 bytes
Tx 9FD770D420DE2C82C2CCCD30F41A442C3D7CCB75222631DC866E3EA0F43DFB28 W1 C2 124389 bytes
Tx 43008081DC3723C73759F71DD09094BF962F09B019CBB91623EA095311DD3D5D W1 C2 12892 bytes
Tx CD55A39D881663508A9340BAFB4E860F016F16CB07BF6D34CF40BF5A62ADF57B W1 C2 21850 bytes
Tx B1C5BAA2593B256068635BBC475E0CC439D66C2DCF12E9DE6F3AAEAF96FF818B W1 C2 51497 bytes
Found 55 oversized witness components in 7607 blocks.
In February I graphed the effect on daily amounts of Blockchain data.
I reviewed this after a few months, in late April:
So in February, Ordinal Inscriptions had a large effect on blockchain data size. This effect seems to be diminishing. Initially there was little impact on numbers of transactions, but this has grown in late April. I thjink there has been a transition in Ordinals Inscriptions from "art" NFTs, some of which were large, to BRC-20 tokens - which are mostly small - around 50 bytes of JSON.
There were less than 100 inscriptions when I asked the question. There are now well over 2,500,000 inscriptions.
