tl;dr
Because of pruning and the limited capabilities of the API, it's almost impossible to determine the current size of the Monero blockchain.
I gave-up on trying to run my own node with a local copy of the blockchain, and I just decided to use the Feather Wallet, which met most of my privacy needs.
internet resources
You can see the monthly growth rate of the monero blockchain since April 2014 on localmonero.co's "Blockchain Growth" section
+---------+----------+
| Month | Size (M) |
+---------+----------+
| 2014-04 | 15.25 |
| 2014-05 | 174.85 |
| 2014-06 | 599.83 |
| 2014-07 | 802.46 |
| 2014-08 | 1030.13 |
| 2014-09 | 1185.65 |
| 2014-10 | 1287.76 |
| 2014-11 | 1371.53 |
| 2014-12 | 1474.86 |
| 2015-01 | 1549.62 |
| 2015-02 | 1621.59 |
| 2015-03 | 1722.08 |
| 2015-04 | 1791.62 |
| 2015-05 | 1857.20 |
| 2015-06 | 1922.23 |
| 2015-07 | 1988.19 |
| 2015-08 | 2055.28 |
| 2015-09 | 2117.14 |
| 2015-10 | 2184.96 |
| 2015-11 | 2240.43 |
| 2015-12 | 2305.43 |
| 2016-01 | 2382.80 |
| 2016-02 | 2452.68 |
| 2016-03 | 2584.14 |
| 2016-04 | 2691.73 |
| 2016-05 | 2770.36 |
| 2016-06 | 2858.08 |
| 2016-07 | 2942.75 |
| 2016-08 | 3079.65 |
| 2016-09 | 3249.86 |
| 2016-10 | 3423.38 |
| 2016-11 | 3572.91 |
| 2016-12 | 3759.68 |
| 2017-01 | 4473.84 |
| 2017-02 | 5504.82 |
| 2017-03 | 6883.35 |
| 2017-04 | 8222.76 |
| 2017-05 | 10269.73 |
| 2017-06 | 12453.46 |
| 2017-07 | 14553.01 |
| 2017-08 | 18365.08 |
| 2017-09 | 20705.24 |
| 2017-10 | 22732.19 |
| 2017-11 | 25274.80 |
| 2017-12 | 28572.24 |
| 2018-01 | 31273.01 |
| 2018-02 | 32970.93 |
| 2018-03 | 34762.09 |
| 2018-04 | 37324.06 |
| 2018-05 | 40179.29 |
| 2018-06 | 42451.55 |
| 2018-07 | 44596.92 |
| 2018-08 | 46625.33 |
| 2018-09 | 48798.78 |
| 2018-10 | 50066.50 |
| 2018-11 | 50688.78 |
| 2018-12 | 51089.53 |
| 2019-01 | 51439.34 |
| 2019-02 | 51709.25 |
| 2019-03 | 52036.94 |
| 2019-04 | 52518.32 |
| 2019-05 | 53389.03 |
| 2019-06 | 54096.73 |
| 2019-07 | 54637.57 |
| 2019-08 | 55211.77 |
| 2019-09 | 55709.73 |
| 2019-10 | 56204.44 |
| 2019-11 | 56778.70 |
| 2019-12 | 57363.47 |
| 2020-01 | 58104.83 |
| 2020-02 | 58741.28 |
| 2020-03 | 59560.46 |
| 2020-04 | 60578.93 |
| 2020-05 | 61684.86 |
| 2020-06 | 62642.85 |
| 2020-07 | 63608.86 |
| 2020-08 | 64714.19 |
| 2020-09 | 65846.84 |
| 2020-10 | 67121.53 |
| 2020-11 | 68294.29 |
| 2020-12 | 69519.75 |
| 2021-01 | 70789.75 |
| 2021-02 | 71886.93 |
| 2021-03 | 73450.93 |
| 2021-04 | 75049.82 |
| 2021-05 | 76565.44 |
| 2021-06 | 77686.56 |
| 2021-07 | 79134.11 |
| 2021-08 | 80871.90 |
| 2021-09 | 82315.42 |
| 2021-10 | 83983.59 |
| 2021-11 | 85858.07 |
| 2021-12 | 87430.51 |
| 2022-01 | 88939.65 |
| 2022-02 | 90230.76 |
| 2022-03 | 91688.47 |
| 2022-04 | 91905.24 |
+---------+----------+
So as of this month, the blockchain size is 91905.24 / 1024 = 89.751210938 GB
source: https://localmonero.co/blocks/stats/blockchain-growth
See also https://monero.stackexchange.com/a/2526/14535
UPDATE: Unfortunately, this is extremely inaccurate
After calculating the blockchain size to be 90G above, I decided to download the monero client with plan on running it on my 128G disk (actually 118G usable). A quick linear extrapolation of the growth over time shows that my disk should be able to fit the monero blockchain until the end of 2024.
So I went ahead and downloaded the monero cli client v0.17.3.0. After weeks of syncing the blockchain, I found the total size on-disk to actually be 129G.
user@host:~$ du -sh /home/user/.bitmonero/lmdb/*
129G /home/user/.bitmonero/lmdb/data.mdb
4.0K /home/user/.bitmonero/lmdb/lock.mdb
user@host:~$
That's wayy over the reported size and it will not fit on my disk :'(
Alternatives
After fighting with the monero blockchain for many months, I looked into alternatives to the core monero wallet.
I finally discovered the Feather Wallet. Compared to most crypto thin wallets, Feather is really, really awesome. It privacy-by-design features eliminated my need to keep a copy of the monero blockchain with me.
⚠ Some monero wallets upload your view key to their severs to eliminate the need to store the monero blockchain! This is done, for example, in MyMonero and Edge.
But the Feather Wallet doesn't upload your view key to their servers. It does download the entire blockchain, but it discards (deletes) any blocks not relevant to your balance. As a result, my Feather Wallet cache only requires a few MB per transaction I make.
Also, feather includes its own tor daemon. It fetches all metadata and publishes all transactions through Tor by default. It doesn't download the blockchain through Tor by default (for speed), but that can be changed in the settings.
IMHO, this was the best win for convince without sacrificing privacy.